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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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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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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Does Heisenberg ferromagnet has inifinite number of phases below the critical temperature?

This is an upshot of the question here. The up-aligned and the down-aligned spin configurations are assumed to be two distinct phases in case of an Ising ferromagnet. But for Heisenberg ferromagnet, ...
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What is the Kitaev Model and why has it become so popular? [closed]

I am seeing Kitaev Model everywhere. It feels like the spin-glass model of our time. How the Kitaev model differ from spin-glass and why it can be used everywhere? Looking at equation 1 here suggests ...
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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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Particular Ising Model of Cellular Automata Shows Mathematical Properties [closed]

I have written a cellular automaton that shows very unusual properties connecting the critical point of 2D square-lattice Ising model and the golden ratio. My question is, is the algebraic method ...
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Interpretation of Ising model simulations

I've been working on numerically solving the Ising model in a study of phase transitions, but I'm having difficulty finding material to help me discuss the results. I'm studying spontaneous ...
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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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Ising Model with site-dependent magnetic field

Consider an Ising system in an external field, which is different at different sites. The Hamiltonian of the system is given by $H = -J\sum_{<i,j>}^{}s_i s_j - \sum_{i}^{} h_i s_i$ Here each ...
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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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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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Majorana zero mode and 1D Ising model

It is known that the one-dimensional (1D) Ising model can be mapped to a free Majorana model using a Jordan-Wigner transformation and its two degenerated ground states are well interpreted by the two ...
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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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Physical explanation of the characteristics of the order parameter of the transverse Ising Model

The Hamiltonian for transverse Ising model is $$\hat{H}=-\sum_{j=0}^{N-1}(\lambda \hat{\sigma}_j^x\hat{\sigma}_{j+1}^x+\hat{\sigma}_j^z)$$ where $\hat{\sigma}$s are Pauli matrices. This model shows ...
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One-dimensional Ising Model in a three spin chain

I have a system of three aligned spins with $S=\frac{1}{2}$. There are interactions between nearest neighbors, and each spin has a magnetic moment. The Hamiltonian of the system is: $$H=J[S_z(1)S_z(2) ...
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Exact Correlation Function of the 2d Ising Problem

I'm working on a variation of the Ising Model for my undergraduate thesis and I need the exact correlation function of neighbouring sites $<\sigma_{1,1}\sigma_{1,2}>$ to compare with my results. ...
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Ising model Monte Carlo simulations in 4D and 5D

I'm going to be simulating the Ising Model in 4D and above to calculate spin-spin correlations and critical exponents and am wondering how to tackle this algorithmically. For example, in 1D, use an ...
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Fixed boundaries in 1D Ising model

What are the differences for solving the one dimensional Ising model for fixed boundaries using the transfer matrix, compared with periodic boundaries? this picture show the solution for periodic ...
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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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Two possible expressions for Hamiltonian of quantum critical Ising chain

While reading an article I encountered an expression for Hamiltonian of so called "critical chain": $$ H = \sum_{k} c^{\dagger}_k[\sigma_x \sin k +B(1-\cos k)\sigma_y]c_k \quad (1)$$ where $c_k$ is ...
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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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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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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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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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Calculating the local energy in neural network quantum state

given a Hamiltonian of Heisenberg 1D model as following: $$H = -J\sum_{I}\sigma_{i}^{z}\sigma_{i+1}^{z}$$ I am trying to solve it with a neural network function given by Restricted Boltzmann machine ...
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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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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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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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Finite temperature spontanous symmetry breaking and Goldstone bosons

I recently asked (and then attemped to answer) a question about spontaneous symmetry breaking in the Heisenberg model: Spontanous symmetry breaking in the Heisenberg model? The question and then the ...
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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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What is the lower critical dimension (LCD) of the bond-diluted Ising model?

It is known that the lower critical dimension (LCD) $d_l$ of the Ising model is $d_l=1$, that the LCD of the Edwards-Anderson model is $d_l=5/2$ (source) and that the LCD of the random field Ising ...
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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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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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A simple model that exhibits emergent symmetry?

In a previous question Emergent symmetries I asked, Prof.Luboš Motl said that emergent symmetries are never exact. But I wonder whether the following example is an counterexample that has exact ...
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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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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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Question about Landau theory of Phase Transitions

The landau theory makes a mean-field approximation on the order parameter, which assumes that there are no fluctuations in the value of the order parameter at different sites (neglects the effects of ...
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Correlation length anisotropy in the 2D Ising model

In the Ising model, the two-spin correlation function is $$ C(\vec{r}) = \langle \sigma_{\vec{r}_0+\vec{r}}\sigma_{\vec{r}_0}\rangle - \langle \sigma_{\vec{r}_0+\vec{r}}\rangle \langle \sigma_{\vec{r}...
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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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