# 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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### 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 ...
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### Examples of important known universality classes besides Ising

I am working with RG and have a pretty good idea of how it works. However I have noticed that even though the idea of universality class is very general and makes it possible to classify critical ...
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### Ising model for dummies

I am looking for some literature on the Ising model, but I'm having a hard time doing so. All the documentation I seem to find is way over my knowledge. Can you direct me to some documentation on it ...
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### Confusion about duality transformation in 1+1D Ising model in a transverse field

In 1+1D Ising model with a transverse field defined by the Hamiltonian $$H(J,h)=-J\sum_i\sigma^z_i\sigma_{i+1}^z-h\sum_i\sigma_i^x$$ There is a duality transformation which ...
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### Mean-field theory : variational approach versus self-consistency

I have a general question concerning mean-field approaches applied to quantum or classical statistical mechanics. Does determining the mean-field by a variational approach always imply that the self-...
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### What is the momentum canonically conjugate to spin in QM?

In Kopec and Usadel's Phys. Rev. Lett. 78.1988, a spin glass Hamiltonian is introduced in the form: $$H = \frac{\Delta}{2}\sum_i \Pi^2_i - \sum_{i<j}J_{ij}\sigma_i \sigma_j,$$ where the ...
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### Time reversal symmetry of transverse field Ising model

Is the transverse field Ising model time-reversal invariant? Specifically consider a non-integrable variant: H = -J \sum_i^{L-1} \sigma_i^z \sigma_{i+1}^z + g \sum_i^L \sigma_i^x + h ...
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### Wick's theorem and transverse field Ising model

I am trying to understand calculation of correlation function in the ground state of the Transverse Field Ising model, from the following book, which is freely available: http://link.springer.com/book/...
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### Percolation in a 2D Ising model

For a 2D Ising model with zero applied field, it seems logical to me that the phases above and below T_c will have different percolation behaviour. I would expect that percolation occurs (and hence ...
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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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### 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 ...
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### Why are large scale structures isotropic in the Ising model?

I have at least a qualitative understanding of why the critical state of the Ising model is scale invariant, by arguments to do with renormalisation, which I understand only very roughly. However, in ...
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### Zero modes $a_j\sim e^{-\kappa j}$ in a semi-infinite quantum Ising chain?

As a way of analyzing the performance of quantum annealing, I've been studying quantum diffusion in fermionizable lattice models with zero modes. In particular, the 1+1D quantum Ising model, semi-...
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### Fermionic Hamiltonian: questions on Bogoliubov transformation and Hermiticity

In section 2.A.2 of Quantum Ising Phases and Transition in Transverse Ising Models by Suzuki, et. al. the authors give the following in their derivation of the Bogoliubov transformation for a ...
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### 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. ...
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### Estimating the Free Energy of a Kink

In statistical mechanics, people often estimate whether or not a certain feature will occur by estimating the feature's free energy. For example, in the 1D Ising model, they want to estimate the ...
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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 ...
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### Critical temperature and lattice size with the Wolff algorithm for 2d Ising model

When I run my implementation of the Wolff algorithm on the square Ising model at the theoretical critical temperature I get subcritical behaviour. The lattice primarily just oscillates between mostly ...
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### What is the difference between classical and quantum Ising model?

The Ising model is defined with the Hamiltonian: $$H = -\sum_{<i,j>}S_i^z\cdot S_j^z$$ What is the difference between quantum version and classical version? My intuition is that the ...
I'm trying to form a better understanding of the 2D Ising Model, in particular the behaviour of the correlation functions between spins of distance $r$. I've found a number of explanatory texts that ...