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A Journey Through Complex Landscapes—Dedicated to Professor Giorgio Parisi to Celebrate the Nobel Prize & His 75th Birthday

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Statistical Physics".

Deadline for manuscript submissions: closed (31 August 2024) | Viewed by 8412

Special Issue Editor

Dr. Giuseppe Florio

E-Mail Website
Guest Editor
Dipartimento di Ingegneria Civile, Ambientale, del Territorio, Edile e di Chimica, Politecnico di Bari, I–70125 Bari, Italy
Interests: statistical mechanics; modeling of macromolecules and bio-inspired materials; quantum correlations

Special Issue Information

Dear Colleagues,

The aim of this Special Issue is bringing together contributions and review articles about recent research activities in the field of complex systems. As a matter of fact, this subject has witnessed an enormous interest in the past years. The features of a complex system typically arise from interactions and competitions among the elementary constituents. As a consequence, the whole system can exhibit peculiar phenomena as nonlinearity, self-organization, and emergence. The field has seen the simultaneous development of new concepts and powerful analytical and numerical mathematical methods. These tools have been used to study models that can be applied to a large number of problems, ranging from collective phenomena in condensed matter physics and biology to climate changes, networks and economic systems.

We welcome articles about concepts and methods in statistical physics with an emphasis on systems with many degrees of freedom. We encourage to submit contributions devoted to analytical and numerical methods. Papers and reviews about spin glasses and applications to materials, soft matter and polymers are welcome. Topics can also include the use of mathematical methods and statistical physics in neural networks (for instance, with applications to machine learning). Papers can also address problems related to biological systems such as biopolymers, folding/unfolding phenomena, formation of structures, cellular mechanics and bioinformatics. Finally, we welcome papers related to quantum properties and phenomena such as quantum correlations in many-body systems and quantum many-body localization.  

Prof. Giorgio Parisi is a leading scientist in the development of methods for the study of complex systems that had large application in research fields involving statistical physics, condensed matter and spin glasses, mathematical physics, biology and collective phenomena. Moreover, Prof. Parisi has made fundamental contributions to the theory of elementary particles, field theory, the study of growth models and the application of stochastic resonance in the study of climatic phenomena. Prof. Parisi's work has earned him the Wolf Prize, the Boltzmann Medal, the Enrico Fermi Prize, the Dirac Medal and, finally, the Nobel Prize in Physics in 2021. This Special Issue is dedicated to him on the occasion of the Noble Prize and his 75th birthday.

Dr. Giuseppe Florio
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • complex systems
  • statistical mechanics
  • spin glasses
  • many-body systems
  • neural networks
  • biological phenomena
  • collective phenomena
  • quantum correlations

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Published Papers (6 papers)

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Research

20 pages, 650 KiB  
Article
The Glass Transition: A Topological Perspective
by Arthur Vesperini, Roberto Franzosi and Marco Pettini
Entropy 2025, 27(3), 258; https://doi.org/10.3390/e27030258 - 28 Feb 2025
Viewed by 375
Abstract
Resorting to microcanonical ensemble Monte Carlo simulations, we study the geometric and topological properties of the state space of a model of a network glass-former. This model, a Lennard-Jones binary mixture, does not crystallize due to frustration. We have found two peaks in [...] Read more.
Resorting to microcanonical ensemble Monte Carlo simulations, we study the geometric and topological properties of the state space of a model of a network glass-former. This model, a Lennard-Jones binary mixture, does not crystallize due to frustration. We have found two peaks in specific heat at equilibrium and at low energy, corresponding to important changes in local ordering. These singularities were accompanied by inflection points in geometrical markers of the potential energy level sets—namely, the mean curvature, the dispersion of the principal curvatures, and the variance of the scalar curvature. Pinkall’s and Overholt’s theorems closely relate these quantities to the topological properties of the accessible state-space manifold. Thus, our analysis provides strong indications that the glass transition is associated with major changes in the topology of the energy level sets. This important result suggests that this phase transition can be understood through the topological theory of phase transitions. Full article
(This article belongs to the Special Issue A Journey Through Complex Landscapes—Dedicated to Professor Giorgio Parisi to Celebrate the Nobel Prize & His 75th Birthday)
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17 pages, 4585 KiB  
Article
Effects of Temperature and Random Forces in Phase Transformation of Multi-Stable Systems
by Giuseppe Florio, Stefano Giordano and Giuseppe Puglisi
Entropy 2024, 26(12), 1109; https://doi.org/10.3390/e26121109 - 18 Dec 2024
Viewed by 762
Abstract
Multi-stable behavior at the microscopic length-scale is fundamental for phase transformation phenomena observed in many materials. These phenomena can be driven not only by external mechanical forces but are also crucially influenced by disorder and thermal fluctuations. Disorder, arising from structural defects or [...] Read more.
Multi-stable behavior at the microscopic length-scale is fundamental for phase transformation phenomena observed in many materials. These phenomena can be driven not only by external mechanical forces but are also crucially influenced by disorder and thermal fluctuations. Disorder, arising from structural defects or fluctuations in external stimuli, disrupts the homogeneity of the material and can significantly alter the system’s response, often leading to the suppression of cooperativity in the phase transition. Temperature can further introduce novel effects, modifying energy barriers and transition rates. The study of the effects of fluctuations requires the use of a framework that naturally incorporates the interaction of the system with the environment, such as Statistical Mechanics to account for the role of temperature. In the case of complex phenomena induced by disorder, advanced methods such as the replica method (to derive analytical formulas) or refined numerical methods based, for instance, on Monte Carlo techniques, may be needed. In particular, employing models that incorporate the main features of the physical system under investigation and allow for analytical results that can be compared with experimental data is of paramount importance for describing many realistic physical phenomena, which are often studied while neglecting the critical effect of randomness or by utilizing numerical techniques. Additionally, it is fundamental to efficiently derive the macroscopic material behavior from microscale properties, rather than relying solely on phenomenological approaches. In this perspective, we focus on a paradigmatic model that includes both nearest-neighbor interactions with multi-stable (elastic) energy terms and linear long-range interactions, capable of ensuring the presence of an ordered phase. Specifically, to study the effect of environmental noise on the control of the system, we include random fluctuation in external forces. We numerically analyze, on a small-size system, how the interplay of temperature and disorder can significantly alter the system’s phase transition behavior. Moreover, by mapping the model onto a modified version of the Random Field Ising Model, we utilize the replica method approach in the thermodynamic limit to justify the numerical results through analytical insights. Full article
(This article belongs to the Special Issue A Journey Through Complex Landscapes—Dedicated to Professor Giorgio Parisi to Celebrate the Nobel Prize & His 75th Birthday)
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10 pages, 364 KiB  
Article
Kramers–Wannier Duality and Random-Bond Ising Model
by Chaoming Song
Entropy 2024, 26(8), 636; https://doi.org/10.3390/e26080636 - 27 Jul 2024
Cited by 1 | Viewed by 1210
Abstract
We present a new combinatorial approach to the Ising model incorporating arbitrary bond weights on planar graphs. In contrast to existing methodologies, the exact free energy is expressed as the determinant of a set of ordered and disordered operators defined on a planar [...] Read more.
We present a new combinatorial approach to the Ising model incorporating arbitrary bond weights on planar graphs. In contrast to existing methodologies, the exact free energy is expressed as the determinant of a set of ordered and disordered operators defined on a planar graph and the corresponding dual graph, respectively, thereby explicitly demonstrating the Kramers–Wannier duality. The implications of our derived formula for the Random-Bond Ising Model are further elucidated. Full article
(This article belongs to the Special Issue A Journey Through Complex Landscapes—Dedicated to Professor Giorgio Parisi to Celebrate the Nobel Prize & His 75th Birthday)
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11 pages, 318 KiB  
Article
Restoring the Fluctuation–Dissipation Theorem in Kardar–Parisi–Zhang Universality Class through a New Emergent Fractal Dimension
by Márcio S. Gomes-Filho, Pablo de Castro, Danilo B. Liarte and Fernando A. Oliveira
Entropy 2024, 26(3), 260; https://doi.org/10.3390/e26030260 - 14 Mar 2024
Cited by 4 | Viewed by 1658
Abstract
The Kardar–Parisi–Zhang (KPZ) equation describes a wide range of growth-like phenomena, with applications in physics, chemistry and biology. There are three central questions in the study of KPZ growth: the determination of height probability distributions; the search for ever more precise universal growth [...] Read more.
The Kardar–Parisi–Zhang (KPZ) equation describes a wide range of growth-like phenomena, with applications in physics, chemistry and biology. There are three central questions in the study of KPZ growth: the determination of height probability distributions; the search for ever more precise universal growth exponents; and the apparent absence of a fluctuation–dissipation theorem (FDT) for spatial dimension d>1. Notably, these questions were answered exactly only for 1+1 dimensions. In this work, we propose a new FDT valid for the KPZ problem in d+1 dimensions. This is achieved by rearranging terms and identifying a new correlated noise which we argue to be characterized by a fractal dimension dn. We present relations between the KPZ exponents and two emergent fractal dimensions, namely df, of the rough interface, and dn. Also, we simulate KPZ growth to obtain values for transient versions of the roughness exponent α, the surface fractal dimension df and, through our relations, the noise fractal dimension dn. Our results indicate that KPZ may have at least two fractal dimensions and that, within this proposal, an FDT is restored. Finally, we provide new insights into the old question about the upper critical dimension of the KPZ universality class. Full article
(This article belongs to the Special Issue A Journey Through Complex Landscapes—Dedicated to Professor Giorgio Parisi to Celebrate the Nobel Prize & His 75th Birthday)
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19 pages, 1151 KiB  
Article
Dynamic Phase Transition in 2D Ising Systems: Effect of Anisotropy and Defects
by Federico Ettori, Thibaud Coupé, Timothy J. Sluckin, Ezio Puppin and Paolo Biscari
Entropy 2024, 26(2), 120; https://doi.org/10.3390/e26020120 - 29 Jan 2024
Cited by 1 | Viewed by 1668
Abstract
We investigate the dynamic phase transition in two-dimensional Ising models whose equilibrium characteristics are influenced by either anisotropic interactions or quenched defects. The presence of anisotropy reduces the dynamical critical temperature, leading to the expected result that the critical temperature approaches zero in [...] Read more.
We investigate the dynamic phase transition in two-dimensional Ising models whose equilibrium characteristics are influenced by either anisotropic interactions or quenched defects. The presence of anisotropy reduces the dynamical critical temperature, leading to the expected result that the critical temperature approaches zero in the full-anisotropy limit. We show that a comprehensive understanding of the dynamic behavior of systems with quenched defects requires a generalized definition of the dynamic order parameter. By doing so, we demonstrate that the inclusion of quenched defects lowers the dynamic critical temperature as well, with a linear trend across the range of defect fractions considered. We also explore if and how it is possible to predict the dynamic behavior of specific magnetic systems with quenched randomness. Various geometric quantities, such as a defect potential index, the defect dipole moment, and the properties of the defect Delaunay triangulation, prove useful for this purpose. Full article
(This article belongs to the Special Issue A Journey Through Complex Landscapes—Dedicated to Professor Giorgio Parisi to Celebrate the Nobel Prize & His 75th Birthday)
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15 pages, 331 KiB  
Article
The Onset of Parisi’s Complexity in a Mismatched Inference Problem
by Francesco Camilli, Pierluigi Contucci and Emanuele Mingione
Entropy 2024, 26(1), 42; https://doi.org/10.3390/e26010042 - 30 Dec 2023
Cited by 2 | Viewed by 1520
Abstract
We show that a statistical mechanics model where both the Sherringhton–Kirkpatrick and Hopfield Hamiltonians appear, which is equivalent to a high-dimensional mismatched inference problem, is described by a replica symmetry-breaking Parisi solution. Full article
(This article belongs to the Special Issue A Journey Through Complex Landscapes—Dedicated to Professor Giorgio Parisi to Celebrate the Nobel Prize & His 75th Birthday)
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