Test of universality in anisotropic 3D Ising model

Abstract

Chen and Dohm predicted theoretically in 2004 that the widely believed universality principle is violated in the Ising model on the simple cubic lattice with more than only six nearest neighbours. Schulte and Drope by Monte Carlo simulations found such violation, but not in the predicted direction. Selke and Shchur tested the square lattice. Here we check only this universality for the susceptibility ratio near the critical point. For this purpose we study first the standard Ising model on a simple cubic lattice with six nearest neighbours, then with six nearest and twelve next-nearest neighbours, and compare the results with the Chen-Dohm lattice of six nearest neighbours and only half of the twelve next-nearest neighbours. We do not confirm the violation of universality found by Schulte and Drope in the susceptibility ratio.

Ising Model Spin S = 1 on Directed Barabási–albert Networks

“…In conclusion, we have presented a very simple equilibrium model on directed Barabási-Albert network [1,2]. Different from the spin 1/2 Ising model, in these networks, the spin 1 Ising model presents a the first-order phase transition which occurs in model with connectivity m = 2 and m = 7 here studied.…”

“…Sumour and Shabat [1,2] investigated Ising models with spin S = 1/2 on directed Barabási-Albert networks [3] with the usual Glauber dynamics. No spontaneous magnetisation was found (and we now confirmed this effect), in contrast to the case of undirected Barabási-Albert networks [4,5,6] where a spontaneous magnetisation was found lower a critical temperature which increases logarithmically with system size.…”

Comparison of Ising Magnet on Directed Versus Undirected Erdös–rényi and Scale-Free Networks

“…They also compared different spin flip algorithms, including cluster flips [12], for Ising-BA networks. They found a freezing-in of the magnetisation similar to [5,6], following an Arrhenius law at least in low dimensions. This lack of a spontaneous magnetisation (in the usual sense) is consistent with the fact that if on a directed lattice a spin S j influences spin S i , then spin S i in turn does not influence S j , and there may be no welldefined total energy.…”

Monte Carlo Methods in Classical Statistical Physics

“…Note that in contrast to the truly universal critical exponents, U * 2p is only weakly universal. By this one means that the infinite-volume limit of such quantities does depend in particular on the boundary conditions and geometrical shape of the considered lattice, e.g., on the aspect ratio r = L y /L x [129,130,131,132,133,134,135,136].…”

“…As emphasized already in Sect. 4.7.1, the cumulants are, however, only weakly universal in the sense that they do depend sensitively on the anisotropy of interactions, boundary conditions and lattice shapes (aspect ratios) [131,132,133,134,135,136].…”