Application of the variational autoencoder to detect the critical points of the anisotropic Ising model
2
Citation
53
Reference
10
Related Paper
Citation Trend
Abstract:
We generalize the previous study on the application of variational autoencoders to the two-dimensional Ising model to a system with anisotropy. Due to the self-duality property of the system, the critical points can be located exactly for the entire range of anisotropic coupling. This presents an excellent test bed for the validity of using a variational autoencoder to characterize an anisotropic classical model. We reproduce the phase diagram for a wide range of anisotropic couplings and temperatures via a variational autoencoder without the explicit construction of an order parameter. Considering that the partition function of $(d+1)$-dimensional anisotropic models can be mapped to that of the $d$-dimensional quantum spin models, the present study provides numerical evidence that a variational autoencoder can be applied to analyze quantum systems via the quantum Monte Carlo method.Keywords:
Autoencoder
Square-lattice Ising model
Ising spin
Cite
Citations (2)
We give a survey of the known results on mixing time of Glauber dynamics for the Ising model on the square lattice and present a technique that makes exact sampling of the Ising model at all temperatures possible in polynomial time. At high temperatures this is well-known and although this seems to be known also in the low temperature case since Kramer and Waniers paper from the 1950s, we did not found any reference that describes exact sampling for the Ising model at low temperatures.
Glauber
Square-lattice Ising model
Square lattice
Lattice (music)
Cite
Citations (0)
The Ising model and its applications,the procedure for deriving the exact solution of the two-dimensional Ising model,the difficulty for solving explicitly the three-dimensional(3D)Ising model have been introduced briefly.The progresses in studying physical properties and critical phenomena of the 3D Ising model by various approximation methods such as the mean field theory and its extensions,renormalization group theory and Monte Carlo simulations etc.have been reviewed.Finally,our recent advances in the conjectures and the putative exact solution of the 3D Ising model are introduced.
Square-lattice Ising model
Cite
Citations (0)
Ising spin
Lattice (music)
Square-lattice Ising model
Cite
Citations (4)
Abstract The Ising model provides an extremely useful example for the investigation of phase transitions. This chapter provides both an introduction to the properties of the Ising model and an overview of the complex phenomena exhibited at phase transitions in general. The one-dimensional model is solved exactly using transfer matrices. Models in higher dimensions are treated in the mean field approximation.
Square-lattice Ising model
Mean field theory
Cite
Citations (1)
The Lenz-Ising model has served for almost a century as a basis for understanding ferromagnetism, and has become a paradigmatic model for phase transitions in statistical mechanics. While retaining the Ising energy arguments, we use techniques previously applied to sociophysics to propose a continuum model. Our formulation results in an integro-differential equation that has several advantages over the traditional version: it allows for asymptotic analysis of phase transitions, material properties, and the dynamics of the formation of magnetic domains.
Square-lattice Ising model
Statistical Mechanics
Basis (linear algebra)
Cite
Citations (1)
The Lenz-Ising model has served for almost a century as a basis for understanding ferromagnetism, and has become a paradigmatic model for phase transitions in statistical mechanics. While retaining the Ising energy arguments, we use techniques previously applied to sociophysics to propose a continuum model. Our formulation results in an integro-differential equation that has several advantages over the traditional version: it allows for asymptotic analysis of phase transitions, material properties, and the dynamics of the formation of magnetic domains.
Square-lattice Ising model
Statistical Mechanics
Basis (linear algebra)
Cite
Citations (0)
Square-lattice Ising model
Statistical Mechanics
Ising spin
Cite
Citations (0)
In this chapter we want to introduce simple importance sampling Monte Carlo techniques as applied in statistical physics and which can be used for the study of phase transitions at finite temperature. We shall discuss details, algorithms, and potential sources of difficulty using the Ising model as a paradigm. It should be understood, however, that virtually all of the discussion of the application to the Ising model is relevant to other models as well, and a few such examples will also be discussed. Other models as well as sophisticated approaches to the Ising model will be discussed in later chapters. The Ising model is one of the simplest lattice models which one can imagine, and its behavior has been studied for a century. The simple Ising model consists of spins which are confined to the sites of a lattice and which may have only the values +1 or −1.
Square-lattice Ising model
Lattice (music)
Cite
Citations (0)
The Ising model is often referred to as the most studied model of statistical physics.It describes the behavior of ferromagnetic material at different temperatures.It is an interesting model also for mathematicians, because although the Boltzmann distribution is continuous in the temperature parameter, the behavior of the usual single-spin dynamics to sample from this measure varies extremely.Namely, there is a critical temperature where we get rapid mixing above and slow mixing below this value.Here, we give a survey of the known results on mixing time of Glauber dynamics for the Ising model on the square lattice and present a technique that makes exact sampling of the Ising model at all temperatures possible in polynomial time.At high temperatures this is wellknown and although this seems to be known also in the low temperature case since Kramer and Waniers paper [KW41] from the 1950s, we did not found any reference that describes exact sampling for the Ising model at low temperatures.
Glauber
Square-lattice Ising model
Square lattice
Lattice (music)
Cite
Citations (2)