Questions tagged [ising-model]

Refers to the mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables that represent magnetic dipole moments of atomic "spins" that can be in one of two states (+1 or −1).

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Some questions about implementing Swendsen-Wang algorithm

I have a lattice system with two types of sites, namely A and B. Both A and B have a possible up or down spin orientation. There exists $J_\textrm{aa,align}/J_\textrm{aa,mis}$, $J_\textrm{bb,align}/...
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What's the most efficient way to obtain the ground state of spin models exactly?

(Note: an earlier version of this question had been asked on Phys.SE before) It is known that finding the ground state of classical spin glasses is NP-hard: it will take (at least) an exponential ...
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Ising model: How can I spot the critical point?

Consider a zero-field Ising model with $N$ spins and periodic boundary conditions, with the Hamiltonian given by: $$H = -K \sum _{(ij)} s_i s_j\tag{1}$$ in 1D and 2D, where $K = \frac{J}{k_BT}$, where ...
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Coupling between 1st and 2nd order phase transitions? [closed]

I am seeking some models or references on how to couple, or what to take into consideration, while coupling first-order phase transitions (for magnetic systems) and second-order phase transitions, in ...
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Why does the Wolff algorithm slow down in a 4-body Ising model?

In the paper that introduced "Self-learning MC" (an ML-inspired MC technique, as I understand) the authors consider a many-body Ising model as an example to show the efficiency of their ...
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Ising models with many-body interactions

I find it surprisingly difficult to find researches/papers on systematic "many-body interaction" extensions of the Ising model. Can somebody tell me a good review/article etc on this matter ...
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How to choose the values of J and spin parameters in a heterogeneous spin system?

In this work, graphene-based systems that are described by mixed spin-3/2 and spin-5/2 are studied using the ising-model. A diagram of the structure is shown bellow: The Hamiltonian used is: \begin{...
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What are good random number generators for Monte Carlo calculations?

Many problems in Computational Physics need the use of random number generators. When studying magnetic materials using the Heisenberg/Ising Hamiltonians (related questions about them can be seen here,...
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What measured quantity can be associated to the value of the J parameter in the Heisenberg/Ising hamiltonians?

This question is related to other one here in the MatterModelingSE: Is it possible to calculate/estimate the value of the J parameter to be used in the Heisenberg/Ising hamiltonians? Here J is the ...
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Is it possible to calculate/estimate the value of the J parameter to be used in the Heisenberg/Ising Hamiltonians?

Studying magnetic systems, two frequently used approximations are the Heisenberg and Ising models (a discussion about these approximations can be read here): \begin{equation} \tag{Heisenberg} \hat{H}...
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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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Is Heisenberg model or in its simplier form Ising model a good approximation to study magnetic systems?

Heisenberg model $$\hat{H}=-\sum_{\langle i j\rangle}J\hat{S}_i\hat{S}_j$$ And in its simplified version, the Ising model $$\hat{H}=-\sum_{\langle ij\rangle}J\hat{S}_i^z\hat{S}_j^z$$ are widely ...
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Where/when did the fields of Operations Research and Spin Physics or Molecular Dynamics begin to cross-pollinate?

Operations Research is a field of mathematics in which optimal or near-optimal solutions are sought for complicated problems. In the modeling of materials, we often optimize Ising models, in which the ...
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