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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.

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8
votes
1answer
542 views

What is the information geometry of 1D Ising model for a complex magnetic field?

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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0answers
488 views

Is this a known entropy formula?

While playing around with a variant of the one-dimensional Ising model with periodic boundary conditions I came up with a formula, let's call it $F$, whose form looks suspiciously like an entropy ...
16
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1answer
410 views

Phase Transition in the Ising Model with Non-Uniform Magnetic Field

Consider the Ferromagnetic Ising Model ($J>0$) on the lattice $\mathbb{Z}^2$ with the Hamiltonian with boundary condition $\omega\in\{-1,1\}$ formally given by $$ H^{\omega}_{\Lambda}(\sigma)=-J\sum_{...
2
votes
2answers
361 views

Identifying a critical phenomena?

I have a system with a number of measurables (in time). Some measurables are discrete some are continuous (within the measurement accuracy). How can I determine whether my system experiences ...
4
votes
1answer
214 views

Convergence of periodic single fermion operators

First, a quick remark: I'm a mathematician, now working on some problems coming from physics (in particular Ising models on quasiperiodic chains). A few things I find rather mysterious. I would ...
47
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5answers
12k views

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 ...
7
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2answers
2k views

Efficiency of Metropolis algorithm

Context is 1D Ising model. Metropolis algorithm is used for simulate that model. Among all possible spins configurations (states) that algorithm generates only states with the desired Boltzmann ...
10
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3answers
1k views

Estimating Partition functions

I have a finite state ensemble with an energy functional (you can think of it as an ferromagnetic Ising model if you like), and I need very careful estimates of the partition function. What methods ...
12
votes
3answers
2k views

Zero magnetization of spin model without external magnetic field

For a given Hamiltonian with spin interaction, say Ising model $$H=-J\sum_{i,j} s_i s_j$$ in which there are no external magnetic field. The Hamiltonian is invariant under transformation $s_i \...
21
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2answers
6k views

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 ...
13
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4answers
2k views

How many Onsager's solutions are there?

Update: I provided an answer of my own (reflecting the things I discovered since I asked the question). But there is still lot to be added. I'd love to hear about other people's opinions on the ...