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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.

134 questions with no upvoted or accepted answers
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0answers
448 views

Measure of Lee-Yang zeros

Consider a statistical mechanical system (say the 1D Ising model) on a finite lattice of size $N$, and call the corresponding partition function (as a function of, say, real temperature and real ...
8
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1answer
598 views

Temperature in the Hamiltonian limit

There is a well known connection between statistical mechanics in D spatial dimensions and quantum field theory in D-1 spatial dimensions. Changing the temperature in statistical mechanics corresponds ...
7
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0answers
505 views

Information geometry of 1D Ising model in complex magnetic field regime

Consider the one-dimensional Ising model with constant magnetic field and node-dependent interaction on a finite lattice, given by $$H(\sigma) = -\sum_{i = 1}^N J_i\sigma_i\sigma_{i + 1} - h\sum_{i = ...
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69 views

What are the excitations in the near critical 2D-Ising model in a magnetic field?

Apparently it is well known that the 2D Ising model with $T=T_C$ in a small magnetic field has a mass gap and correlation length $\xi \sim h^{- \frac{8}{15}} $. Further, in a paper in 1989 ...
5
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2answers
201 views

APS $\eta$-invariant and spin-Ising TQFT

I am interested in the relation between the Atiyah-Patodi-Singer-$\eta$ invariant and spin topological quantum field theory. In the paper Gapped Boundary Phases of Topological Insulators via Weak ...
5
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1answer
12k views

Force from solenoid

I'd like to approximate the force from a solenoid, or at the very least find a formula which is proportional to the force so that I can experimentally find the constant for my particular case. ...
4
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0answers
85 views

Renormalization Group - Scaling fields and physical critical exponents (1D Ising model)

This is related to this question: Critical exponents and scaling dimensions from RG theory. TLDR: How to compute physical critical exponents $\alpha, \beta, \gamma, etc$ from the RG exponents when ...
4
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208 views

Maximum value of the microcanonical distribution for the finite 2D Ising model

Here's an interesting combinatorial problem relating to the two-dimensional N x N Ising model, whose energy is given by $$E=-\sum_{(i,j)pairs} Js_is_j, $$where the value of nearest-neighbor cells are $...
4
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361 views

Critical temperature difference between Ising and XY model

The following formula gives the critical coupling (more precisely the ratio of the spin-spin coupling over the temperature) for $O(n)$ models on a triangular lattice: $$\text{e}^{-2K}=\frac{1}{\sqrt{...
4
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0answers
172 views

What real experimental systems are well-described by Glauber-Ising spins?

I'm hoping for references to actual physical systems in which all or at least most of the following can be simultaneously characterized: the spin flip rate, the temperature, and a relaxation or ...
3
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47 views

Correlation length amplitudes in Ising 2D model

I am reading the article about Universal amplitude ratios in the 2D Ising model (https://arxiv.org/abs/hep-th/9710019) by G. Delfino. I have a question about page 3 of the paper. For a magnetic ...
3
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77 views

What happens to the dynamical critical exponent in the quantum-classical mapping?

It is well-known that one can, e.g., map the classical 2D Ising model to the 1D quantum Ising chain. Moreover, their critical points are related. Hence, if one is interested in critical exponents ...
3
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93 views

How do WZW coset models contain perturbations?

I've been studying the coset construction. As far as I understand it, the Sugawara energy momentum tensor is a way of embedding the virasoro algebra inside the Lie algebra of your original WZW model. ...
3
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65 views

A proof for this equivalent version of the Infrared Bound/Gaussian Domination

Consider the Ising Model in the $d$-dimensional discrete torus with side lengh $L$, denoted by $\mathbb{T}_L $, with nearest neighbors interaction (with interaction parameter $J$, no magnetic field, ...
3
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595 views

A question in Quantum Phase Transition of Transverse Ising Model

In section 1.4 quantum Ising model of Subir Sachdev's book Quantum Phase Transitions, he discusses the quantum phase transition of transverse quantum Ising Model at zero temperature (so we just focus ...
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151 views

Ising CFT on a higher genus surface

I'm wondering if someone knows how to put the critical Ising model on an arbitrary Riemann surface of genus g. I know how to do it on a torus but I want to know how to find the correlator of the Ising ...
3
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151 views

Majorara zero mode in Ising chain, not exactly zero subtlety

We know the transverse field Ising model with N sites(open boundary), can be mapped into N free fermions(there are 2N modes if including the negative energy counterparts) With property: $$\gamma^\...
3
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1answer
216 views

Ising model as quantum model?

I've read in a few papers things that use the fact that the $2D$ Ising model can be interpreted as a $1+1$ quantum spin model. I haven't been able to find this description and would like to read about ...
3
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565 views

Transfer from Heisenberg to Ising model

It is well know, that ferromagnets can be described using Hamiltonian $$ H = -\sum\limits_{i<j}J_{ij}\, (\mathbf{s}_i \cdot \mathbf{s}_j). $$ where (three dimensional) spins $\mathbf{s}_i$ ...
3
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0answers
631 views

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 ...
3
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126 views

Is there a reasonable lower bound for free energy per site of the 2D Ising model in the presence of an external field?

Given the standard Ising partition function: $$Z(\theta ,h) = \sum\limits_{\bf{x}} {\exp \left\{ {\theta \sum\limits_{(i,j) \in E} {{x_i}{x_j}} + h\sum\limits_{i \in V} {{x_i}} } \right\}}, $$ is ...
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265 views

Motivation of the Heisenberg model of ferromagnetism

In the Heisenberg model of ferromagnetism the atoms are assumed to be arranged in a lattice. The $i$-th atom has a spin operator $\vec S_i$ (here $i$ belongs to the lattice). The Hamiltonian is given ...
3
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201 views

Monte Carlo for Random Bond Ising ferromagnet

The set-up: Consider the Ising model on an $L \times L$ square lattice, where the coupling of each bond is chosen to be $+J$ (ferromagnetic) with probability $(1-p)$ and $-J$ (antiferromagnetic) with ...
3
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107 views

Question about the derivation of an equation in full replica symmetry breaking solution

Using replica method and saddle point method, the free energy of a magnetic system can be expressed as $$-\beta[f]=\lim_{n\to0}\{\frac{-\beta^2J^2}{4n}\sum_{a\ne b}q_{\alpha\beta}^2-\frac{\beta J_0}{...
2
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34 views

Eigenfunctions and eigenvalues XY Ising model

In the XY Ising model we have the following Hamiltonian: $$H=-J\sum_i \cos(\theta_i-\theta_{i+1}).$$ From this I found that $\langle \theta_i| T | \theta_{i+1}\rangle = \exp(\beta J \cos(\theta_i-\...
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38 views

Mathematical Rigorousness of Taking the Thermodynamical limit of a finite size quantum model

Suppose I have nearest Neighbour Quantum Ising model with a transverse field. $$\hat{H} = \sum_{i}S^{x}_iS^{x}_{i+1} + h\sum_i S^{z}_i$$ Through Jordan-Wigner and Bogoliubov transformation, one finds ...
2
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1answer
44 views

Magnetic susceptibility error by binning Monte Carlo

I am studying the 2D Ising model using Monte Carlo simulations and I have learned the binning (or batching) method for the error statistical analysis. Following this discussion https://books.google.it/...
2
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40 views

How to quantify frustration for spin models with long range interactions?

Consider the following Hamiltonian: $$ H=-\sum_{i\neq j}J_{ij}S_iS_j-\sum_i H_iS_i $$ where $S_i\in\{-1,1\}$, and the summed pair $i,j$ can be any two distinct indices (not necessary adjacent spins)....
2
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0answers
68 views

Elitzur theorem and the Ising model

I was recently studying the Elitzur theorem and its application to the Ising model on Kogut: An introduction to lattice gauge theories and spin systems, chapter $5$C. I was wondering how he obtain $\...
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0answers
128 views

Block diagonalizing a Hamiltonian using a symmetry

I have the following Hamiltonian, describing the 3 state Chiral clock model in 1D: $$H = -f \sum_{j=1}^L (\tau_j^\dagger e^{-i \phi}+h.c.)-J\sum_{j=1}^{L-1}(\sigma_j^\dagger\sigma_{j+1}e^{-i\hat{\phi}}...
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39 views

Software that can perform QMC on quantum Ising model

I'm trying to find a software that can perform QMC using the loop algorithm as outlined in the following lecture notes: https://www.cond-mat.de/events/correl13/manuscripts/wessel.pdf The closest ...
2
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0answers
65 views

Correlation functions of exactly solvable 1D quantum models

Quantum 1d spin-1/2 transverse Ising and XY models are both related to 2d classical Ising model. Are there any known simple explicit relations between correlation functions of this models? Something ...
2
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1answer
145 views

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 ...
2
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0answers
94 views

Peierl's Proof on Spontaneous Magnetization

How to modify Peierls proof to show that, for the Ising model on the hexagonal lattice with nearest neighbor ferromagnetic coupling $J$, at low temperatures there is a spontaneous magnetization?
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206 views

Transfer Matrix formalism

I am trying to apply the transfer matrix formalism to an Ising model problem, and am having some difficulties deriving the correct matrix to use. The problem is as follows. There is an infinite chain ...
2
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0answers
108 views

The Ising approximation - what exactly is it?

I am slightly confused about the nature of the Ising model to study ferromagnetism. Consider the Heisenberg Hamiltonian with Zeeman term: \[H=-\frac{1}{2} \sum_{i\ne j}J_{ij} S_i\cdot S_j+g\mu_B {B}\...
2
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0answers
113 views

Finding recursion relation in renormalization group theory

I'm trying to learn statistical mechanics by studying the book by Plischke and Bergersen, but I'm stuck with how to find the recursion relation (which can be used to find the fixed points) in ...
2
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1answer
347 views

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 ...
2
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0answers
112 views

Intuition on Gibbs measures

I am (roughly) aware of the way Gibbs measures are used to solve physical systems (e.g. the Ising model). We can basically boil it down to pinpointing a Hamiltonian. My question is, consider a ...
2
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0answers
58 views

Thermodynamics for 1D line of 3D dipoles

The 1D Ising model was solved almost a century ago. This model assumed spins that point along the 1D line to the left or right and only considered nearest neighbors, so that the Hamiltonian with no ...
2
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0answers
275 views

Ising model at high vs. low temperature

The output of the Ising model over a 2D binary lattice looks to have spin states uniformly distributed over the lattice for high values of the temperature parameter with the output attaining ...
2
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0answers
349 views

Books/resources for statistical field theory

I was wondering if anyone knows good, approachable textbook or other resources about statistical field theory (topics like in Kardar's Statistical physics of fields: lattice models, mean field theory, ...
2
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0answers
54 views

Filling ising model with basis

This questions involves how to fill a lattice with ordered basis: Is there some established mathematical approach in filling a physical lattice with some colored basis (black and white here)? For ...
2
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0answers
210 views

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, ...
2
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0answers
377 views

Spontaneous symmetry breaking in the quantum 1D XX model?

The ground states of the quantum 1D Ising and Heisenberg models exhibit spontaneous magnetization. Is this also true for the 1D XX model?
2
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0answers
181 views

Spin Glass Transitions in Random Bond Ising Model (RBIM)

In brief, is there a list of spin glass transition properties for the RBIM on different lattices? Is there any know results about the relationships between these probabilities for a graph and its dual?...
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0answers
61 views

Critical exponent mean field Ising model

I am given the following expression for the free energy: $$f = \frac{1}{2}r_0 m^2+um^4+vm^6,$$ where $r_0=k_B (T-T_c)$ with $T_c$ the critical temperature and $u=\frac{1}{12}k_B T$ and $v=\frac{1}{...
1
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0answers
62 views

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 ...
1
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0answers
24 views

Why do the Binder Cumulants of different system sizes intersect at the critical point?

When Monte Carlo simulations are performed for spin models (Ising model etc.) the critical temperature can be found by simulating for different lattice sizes and plotting the Binder Cumulant for them. ...
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0answers
43 views

Asymmetric hysteresis loop in Ising Model

I am doing simulations using Monte Carlo of the 2 dimensional square lattice with periodic boundary conditions Ising model, and i obtain hysteresis loops, which are asymmetric. Meaning i obtain a ...