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Entropy 2018, 20(8), 585; https://doi.org/10.3390/e20080585

Investigation of Finite-Size 2D Ising Model with a Noisy Matrix of Spin-Spin Interactions

Scientific Research Institute for System Analysis, Russian Academy of Sciences, 117218 Moscow, Russia
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Received: 20 June 2018 / Revised: 13 July 2018 / Accepted: 2 August 2018 / Published: 7 August 2018
(This article belongs to the Special Issue Entropy and Complexity of Data)
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Abstract

We analyze changes in the thermodynamic properties of a spin system when it passes from the classical two-dimensional Ising model to the spin glass model, where spin-spin interactions are random in their values and signs. Formally, the transition reduces to a gradual change in the amplitude of the multiplicative noise (distributed uniformly with a mean equal to one) superimposed over the initial Ising matrix of interacting spins. Considering the noise, we obtain analytical expressions that are valid for lattices of finite sizes. We compare our results with the results of computer simulations performed for square N = L × L lattices with linear dimensions L = 50 ÷ 1000. We find experimentally the dependencies of the critical values (the critical temperature, the internal energy, entropy and the specific heat) as well as the dependencies of the energy of the ground state and its magnetization on the amplitude of the noise. We show that when the variance of the noise reaches one, there is a jump of the ground state from the fully correlated state to an uncorrelated state and its magnetization jumps from 1 to 0. In the same time, a phase transition that is present at a lower level of the noise disappears. View Full-Text
Keywords: Ising model; noisy connections; ground state; free energy; internal energy; magnetization; specific heat; entropy; critical temperature Ising model; noisy connections; ground state; free energy; internal energy; magnetization; specific heat; entropy; critical temperature
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Kryzhanovsky, B.; Malsagov, M.; Karandashev, I. Investigation of Finite-Size 2D Ising Model with a Noisy Matrix of Spin-Spin Interactions. Entropy 2018, 20, 585.

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