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.

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Value of critical exponent $\alpha$ for 2D ising model

The Onsager solution for specific heat is $$C\approx -Nk\frac{2}{\pi}\bigg(\frac{2J}{kT_c}\bigg)^2\ln\Big|1-\frac{T}{T_c} \Big|\qquad (T \textrm{ near } T_c)$$ Critical exponent $\alpha\neq 0$. ...
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Autocorrelation function problem in Monte Carlo simulation of 2D Ising model

Currently, I did a Monte Carlo simulation with the local update and Wolff cluster updated in 2D classical Ising model. I use the autocorrelation function to compare 2 different algorithm in critical ...
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Nonzero spontaneous magnetization in two-dimensional Ising model

The two-dimensional Ising model with the nearest-neighbour interactions enjoys a $\mathbb{Z}_2$ symmetry under $S_i\to -S_i$; it displays sponatebous symmetry breaking at a finite temperature $T_C=2J[...
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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 ...
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Simple Quantum Monte Carlo question

Currently I am doing some simple simulation of 1D Transverse field Ising model. I map the quantum mechanical problem into classical 2D classical Ising model with different horizontal interaction and ...
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Numerical renormalization of 2D Ising lattice

I'm trying to make some toy computations on the $2D$ Ising model on a square lattice. I want to apply a renormalization transformation, and try to estimate observables on the renormalized lattice ...
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What is the ground state wavefunction of $\hat{H}=-J\sum\limits_{\langle i,j\rangle}\hat{S}_i^z\hat{S}_j^z,~~ (J>0)$?

The hamiltonian of a collection of noninteracting quantum spin-$1/2$ operators $\hat{S}_i$ fixed at each lattice site $i(=1,2,..., N)$ in presence of magnetic field ${\bf B}=B\hat{{\bf z}}$ $$\hat{H}=-...
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Averages of absolute values in Monte Carlo simulation of Ising Model

Consider the 2D Ising model in $0$ field, with Hamiltonian $$ H=J\sum_{\langle i,j\rangle}\sigma_i\sigma_j$$ The magnetization per spin is defined as $$M=\frac{1}{N}\sum_i \sigma_i $$ Where $N$ is ...
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Needed Clarification: In Calculation of specific heat of Ising model (Simulation)

I am want to calculate the specific heat for 2D 100x100 square lattice ising model. I have calculated the correlation time, viz., $\tau$. Now I want to calculate the specific heat and error in ...
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Derivation of expected value of a function from master equation Glauber Model (Ising Model)

Let $\sigma =(\sigma_1, \sigma_2,...,\sigma_N)$ where $\sigma_i =\pm \sigma_i$. Let also $\sigma^i =(\sigma_1, \sigma_2,...,-\sigma_i, ...,\sigma_N)$. Given the master equation: \begin{equation} \...
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Fourier transform of fermionic creation/annihilation operator

How should I picture the Fourier transform of a fermionic creation (annihilation) operator acting on a site of a periodic, say one-dimensional, lattice? I mean, in a real-space picture, what are the ...
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What do physicists mean by solving the Ising model?

To me, an Ising model is a setting of discrete objects, that have attributes (spins) that contribute to energy based on interactions with nearby objects. With the energy function (Hamiltonian) written ...
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1D Ising Model with magnetic field on even sites: Transfer Matrices

I have been trying to work out a practice problem after reading about Transfer Matrices method for solving 1D Ising Model. Please, if you are able to, tell me whether the way I introduced transfer ...
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On the quantum computer implementation of FFT

In Fig. 1 of the paper Exact Ising model simulation on a quantum computer, it appears a circuit to implement a Bogoliubov and (discrete) fast Fourier transform (FFT) over 4 qubits in order to ...
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Magnetization in Quantum Transverse Ising Model: Mean Field Theory vs Reality

One of the canonical examples of mean field theory concerns the ground state ($T=0$) of the transverse field Ising model, with Hamiltonian $$H = -J\sum_{<ij>} \sigma^z_i \sigma^z_j-h \sum_i\...
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Ising universality class

Ising model is defined as lattice model with interactions only between nearest sites if lattice. If we deform Ising model, include non-nearest interactions or interactions between more than two ...
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Partition function for quantum Ising model

I have hamiltonian for fermionic field as $${\cal H}_F=E_0+\int dx[\frac{v}{2}(\Psi^\dagger\frac{\partial \Psi^\dagger}{\partial x}-\Psi\frac{\partial \Psi}{\partial x})+\Delta\Psi^\dagger\Psi]\tag{1}$...
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Typical cluster size in ising model

What is typical cluster size in two dimensional ising model. By cluster size I mean size of domain. Can I call correlation length of spin-spin correlation to be typical size of clusters. Is the ...
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The well-defined temperature and 0D Ising model (Ref. Shankar)

I’m reading Shankar’s book Quantum field theory and condensed matter. On page 17, these two bold sentences seem to contradict each other: The system in contact with the heat bath and described by Z ...
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Effective hamiltonian method for the quantum Ising model

I am reading Subir Sachdevs book on quantum phase transitions (second edition). In chapter 5 (page 58) he defines a hamiltonian $H=H_0+H_1$ where the eigenstates of $H_0$ are known and the influence ...
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1D Ising Model model montecarlo metropolis algorith simulation with external fields

Hi everyone, this is a simple simulation of the Ising model in 1D case, the algorithm is the well known metropolis one, the only difference is that I want to take into account an external magnetic ...
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Ferromagnetic/Paramagnetic Phase Transition in a Non-Zero External Magnetic Field

I'm new to condensed matter theory, especially spin-glass systems. I understand that the Ising model exhibits a Phase Transition when there is no external magnetic field (h=0). And that at the ...
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1D linear spin-chain for Ising model

In section 2.1 of the article https://arxiv.org/abs/1807.07112 appears the following Hamiltonian for a 1D chain of $n$-spins $$ H = \sum_{i = 1}^n \sigma^x_i\sigma^x_{i + 1} + \sigma^y_1\sigma^z_2···\...
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Fluctuating magnetization curve in ising model

I am working on Metropolis-Montecarlo algorithm for 2D Ising model in python partly based on this document. I ran the simulation for 100 times on a 25 x 25 lattice with external magnetic field B = 0. ...
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Torus two-point blocks and a-monodromy for the 2D Ising CFT

I was trying to use some concrete example to understand the a-monodromy and b-monodromy in the proof of the Verlinde formula. On the Yellow Book, I found the following results for the torus two-point ...
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Phase transition in ground state of a ferromagnetic system

I am new to this topic of phase transition , but is the phase transition occurs in the ground state of the ferromagnetic system ? As we get the self consistent equation of local magnetization (m) by ...
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Question about Peierls Droplets argument

I am trying to understand the logic of considering Peierls droplets. The basic idea is that the entropy and energy of the loop are proportional to its length L (see Tong's lectures, p.161). As a ...
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One dimensional phase transitions

Due to R. Peierls argument there is not phase transitions is one dimensional lattice systems. Argument in $d=1$ goes like that: flipping of one spin in system of N spins will lead to change of free ...
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Ising model operators

Ising model formulated as lattice theory with local degrees of freedom described by $s_i$ $i\in 1, \dots, N$ and energy: $$ E[\sigma_i] = -J\sum_{<ij>} s_i s_j $$ From $s_i$ I can construct a ...
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Near spin expectation value in the 2D classical ising model

I am looking at McCoy's book about on Ising model because I am looking for the expectation value of two adjacent spins at the critical temperature in the infinite volume limit of the anisotropic Ising ...
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Good resourse for Ising Problem Model

I am student of mathematics, and I will wrote theoretical article about Ising problem in Adiabatic Computation. Do you have a good resource where it is good explaining? In my context I have ...
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Three point correlation function 2D Ising model

What is the expected behaviour of the three point function $<\sigma_i \sigma_j \sigma_k>$ of the Ising 2D model at the critical point where conformal symmetry is valid? Do they have a power-law ...
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What's the point of observing independent samples in Ising Model for a Monte Carlo simulation?

Something about the uncorrelated samples of observations in Markov Chain Monte Carlo(MCMC) simulation of my Ising model has been confusing me. Before I start asking my question, I'll first describe ...
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Ising model 1D spontaneous magnetisation

What does it mean to 'compute the spontaneous magnetisation'? According to wikipedia: 'Spontaneous magnetization is the appearance of an ordered spin state (magnetization) at zero applied magnetic ...
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Various questions on renormalization in lattice systems

Forgive the long, multi questioned-question. The setting of this question is inspired by this answer. Consider some theory on a lattice, for example the 2D $0$-field Ising model $$H=-K\sum_{\langle i,...
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Correlation time for Ising metropolis algorithm as a function of temperature

I am using metropolis algorithm for 2D Ising Model. Is there an expression for correlation time of consecutive Monte Carlo sweeps as a function of temperature? The external magnetic H field is set to ...
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Is there a spontaneous symmetry breaking in finite-size Ising model with + boundary condition?

My question is related to Chapter 3 of Prof. Yvan Velenik's book "Statistical Mechanics of Lattice Systems: a Concrete Mathematical Introduction". For an Ising model defined on a finite volume $\...
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Partition function of 2D Ising model on a squared lattice in the canonical ensemble in the low temperature limit

I'm currently working through David Tong's script on statistical mechanics (http://www.damtp.cam.ac.uk/user/tong/statphys/sp.pdf) and came across something that I don't quite understand (page 166). ...
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1d Ising model: energy inside domains

I am trying to understand some calculations to get the excitation energy $\Delta E_\text{M} = E_\text{M} - E_0$ (M is the number of domain walls) in the 1d Ising model in the absence of a magnetic ...
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Show equation equivalent in RG of 1d Ising Model

I know the Ising model is given by $$Z= \sum_{\sigma_i=\pm 1} e^{-F + J \sum_i \sigma_i \sigma_{i+1} - h\sum_i \sigma_i}$$ and that if h=0I can sum over even spins and get the partition function ...
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Wick-rotated quantum computers e.g. to be realized with Ising-like systems?

Quantum mechanics is equivalent with Feynman path ensemble, which after Wick rotation becomes Boltzmann path ensemble - and e.g. Ising model is a basic condensed matter model, which is assumed to use ...
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Feynman's corrective term in his approach to the Onsager Problem

I am studying Feynman's book: 'Statistical Mechanics: A set of lectures' and his approach to the Onsager problem(Section 5.4). In the subsection 'Method of Calculating partition Function', Feynman ...
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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 ...
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Violation of Bell-like inequalities with spatial Boltzmann path ensemble: Ising model?

Quantum mechanics is equivalent with Feynman path ensemble, which after Wick rotation becomes Boltzmann path ensemble, which can be normalized into stochastic process as maximal entropy random walk (...
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Recursion method 1D Ising model in zero-field

Good day to you all, I'm currently reading Goldendfeld's lectures on phase transitions, and I'm a bit perplexed by a formula appearing in section 3.1.3 of the book. He starts with the partition ...
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Hammersley-Clifford theorem and maximal entropy random walk for Ising-like models?

It seems that condensed matter people usually just brute force use Monte-Carlo, but there are some subtle mathematical tools which might be worth considering, for example: 1) Hammersley-Clifford ...
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Is there a way to perform Ising model simulations with a Game of Life approach?

This question may turn out to be trivial or nonsensical as I do not have more than undergraduate understanding of both the Ising model and computational physics simulations. I just wanted to post ...
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Mean field solution of the Ising Model

I try to compute the variational free energy in the Ising Model using the bogoliubov inequality: \begin{equation} \mathcal{F}(\lambda) = F_{0}(\lambda) \ + \ \langle\mathcal{H_{1}(\lambda)} \rangle_{...
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Minimal models and Lattice models

How does one see that the minimal model M(4,3) is the Ising model ? And how can I argue out that the fields contained in M(6,5) but with the non-diagonal modular invariant partition function ...
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Using MATLAB to simulate the Ising Model [closed]

I am using MATLAB to simulate a 1D Ising Chain. I am running into an issue where when trying to find heat capacity, my system has a tremendous amount of noise. I'll post my code and an image of the ...

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