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It is rigorously proved that at any nonzero temperature, a one- or two-dimensional isotropic spin-$S$ Heisenberg model with finite-range exchange interaction can be neither ferromagnetic nor antiferromagnetic. The method of proof is capable of excluding a variety of types of ordering in one and two dimensions.
We consider an Ising model in which the spins are coupled by infinite-ranged random interactions independently distributed with a Gaussian probability density. Both "spinglass" and ferromagnetic phases occur. The competition between the phases and the type of order present in each are studied.
Abstract This book provides an introduction to Monte Carlo simulations in classical statistical physics and is aimed both at students beginning work in the field and at more experienced researchers who wish to learn more about Monte Carlo methods. The material covered includes methods for both equilibrium and out of equilibrium systems, and common algorithms like the Metropolis and heat-bath algorithms are discussed in detail, as well as more sophisticated ones such as continuous time Monte Carlo, cluster algorithms, multigrid methods, entropic sampling and simulated tempering. Data analysis techniques are also explained starting with straightforward measurement and error-estimation techniques and progressing to topics such as the single and multiple histogram methods and finite size scaling. The last few chapters of the book are devoted to implementation issues, including discussions of such topics as lattice representations, efficient implementation of data structures, multispin coding, parallelization of Monte Carlo algorithms, and random number generation. At the end of the book the authors give a number of example programs demonstrating the applications of these techniques to a variety of well-known models.
We present a data-driven pipeline for model building that combines interpretable machine learning, hydrodynamic theories, and microscopic models. The goal is to uncover the underlying processes governing nonlinear dynamics experiments. We exemplify our method with data from microfluidic experiments where crystals of streaming droplets support the propagation of nonlinear waves absent in passive crystals. By combining physics-inspired neural networks, known as neural operators, with symbolic regression tools, we infer the solution, as well as the mathematical form, of a nonlinear dynamical system that accurately models the experimental data. Finally, we interpret this continuum model from fundamental physics principles. Informed by machine learning, we coarse grain a microscopic model of interacting droplets and discover that nonreciprocal hydrodynamic interactions stabilize and promote nonlinear wave propagation.
Progress of Theoretical Physics Vol. 58 No. 1 (1977) pp. 77-91 The Mode-Coupling Theory for the Nematic Mesophase near the Clearing Point Yasuhiro Shiwa
Progress of Theoretical Physics Vol. 49 No. 1 (1973) pp. 83-88 Critical Properties of Ising Models Containing Dilute Impurities Takeo Osawa and Katuro Sawada Progress of Theoretical Physics Vol. 50 No. 4 (1973) pp. 1232-1239 Critical Properties of Ising Models Containing Dilute Impurities. II Katuro Sawada and Takeo Osawa
Fumiaki Shibata, Kazushige Machida, Hiroshi Mamada; Equivalence of s-d Exchange, Anderson and Wolff Models, Progress of Theoretical Physics, Volume 45, Iss