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Questions tagged [ising-model]

The Ising model of ferromagnetism in statistical mechanics consists of discrete bimodal (+1 or −1) "spin" (moment) variables in a simple Hamiltonian interacting with their next neighbors on a lattice. The one-dimensional variant does not evince a phase transition, but the two-dimensional square-lattice one does. Use for analog and generalized discrete models on several lattices and dimensions.

The Ising model of ferromagnetism in statistical mechanics consists of discrete bimodal (+1 or −1) "spin" (moment) variables in a simple Hamiltonian interacting with their next neighbors on a lattice. By dint of simplicity, it is relatively easy to solve explicitly as a function of the interaction strength: The one-dimensional variant does not evince a phase transition, but the two-dimensional square-lattice one does.

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Why is it hard to solve the Ising-model in 3D?

The Ising model is a well-known and well-studied model of magnetism. Ising solved the model in one dimension in 1925. In 1944, Onsager obtained the exact free energy of the two-dimensional (2D) model in zero field and, in 1952, Yang presented a…
Marton Trencseni
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Exact solution of the 2D Ising model in an external magnetic field?

The 2D Ising model is a thoroughly studied model. One of the remarkable features of the model is that it predicts a hysteresis. However, I cannot seem to find the appropriate literature on this subject. I did do searches on Scopus to find relevant…
JBrouwer
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Non-homogeneous Ising model in one dimension

In formula of Hamiltonian for Ising model in one dimension we have $J_{ij}$. usually, we take $J_{ij}$ as a constant. In this way it is called homogeneous Ising model. My question is if we take $J_{ij}$ as a variable depends on sites $i$ and $j$ in…
Rose
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Ising model - Two different Gibbs distributions? (Friedli-Velenik)

I am currently reading the book Statistical Mechanics of Lattice Systems by Friedli-Velenik. Given a finite set $\Lambda\subset\mathbb Z^d$ there are two definitions of the Hamiltonian (with empty boundary condition) appearing in the book and I…
Filippo
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How to use Ising Spin model for prediction of time series "Phase"

I am investigating a 2d Ising Spin Lattice. I have been able to generate a Monte Carlo app that gives me the changing spin matrix through my iterations - like the many examples on the web. However, I am trying to predict an independent variable…
ManInMoon
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1d Ising model specific heat and susceptibility

I made some plots for 1d Ising chain with finite N, and it seems like there is always a maximum of specific heat and susceptibility at certain temperature. As the N gets larger and larger, the maximum moves to T=0. We know there is no phase…
lol
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Decomposition of $\mu^{free}$ for the Ising-Dyson Model

For the nearest neighbours Ising-Model in any dimension, it is known that $$ \mu^{free}_\beta= \frac{1}{2} \mu^{+}_\beta+\frac{1}{2} \mu^{-}_\beta $$ for any inverse of temperature $\beta>0$. Is the same valid for dimension $d=1$, with a…
Kernel
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Finite temperature transverse magnetization in transverse Ising model

Consider the transverse field Ising model, with $H=-J\sum_i\left(\sigma^x_i\sigma^x_{i+1}+g\sigma^z_i\right)$ What happens to the expectation value of the magnetization $\langle\sigma_z\rangle$ at finite temperature? Can anyone give me a ref?
poiuyt rewq
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Formula for the energy per site in the triangular Ising model

I'd like to check the correctness of a simulation I ran on the Ising model on a triangular by verifying if I get the good value of the mean energy per site. I found a formula giving it for high temperatures on a square lattice but nothing on the…
Learning is a mess
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Is it possible to find the ground state of generalized Ising models?

Is there a general solver (or a theoretical algorithm) for obtaining the ground state configuration of the extended Ising model, which involves an arbitrary lattice, arbitrary coordination number (i.e. $n$-body interactions for arbitrary $n$),…
user40780
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What is a "transient state" and "transition state" in Ising model?

I was analyzing this source code of the Ising model. I found the term "transient state". I also found the term in this text: There are two absorbing states in this Markov chain because once either Jane or Eddie wins, the game is over, and the die…
user280949
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What is after the Ising model?

If this model is solved in three dimensions, Will there be additional research on it? Like what? Does this open the way to solve other models? Like what?
user283629
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1D ising system: reducing configuration with respecet to symmetry and total magnetization

this question is mathematical in its sense and considers the following 1D ising spin model $$s_1s_2s_3....s_{n-1}$$ where $s_i=\pm 1$. I would like to find the total number of different configurations after reducing symmetry and 'total…
jarhead
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What happens to the energy when a system following Ising Model goes to its ground state?

I'm a computer scientist and new to Ising Model. I've learned that if such a system is left to itself it will converge to its minimum energy state. Here are the questions I have: As the system is going toward its minimum energy, where does the…
al pal
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Applications of Sampling from SK Ising Model

I have written a program for Monte Carlo sampling from Sherrington-Kirkpatrick (SK) Ising model. I have two questions about it: 1- What are some applications of it? I already know training Boltzmann machines and solving optimization problems can be…
Farzad
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