Questions tagged [spin-models]
A mathematical model used in physics primarily to explain magnetism.
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Mathematical meaning for Algebraic Bethe Ansatz
I'm a mathematician who's trying to understand the meaning of Algebraic Bethe Ansatz. What I understood is that when dealing with quantum integrable models (like XXZ Heisenberg spin chain), one is ...
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Trying to understand Kitaev's calculation of relative Majorana number in two dimension
In appendix C.4.3 of "Anyons in an exactly solved model and beyond", Kitaev provides a proof of the fact that when the Chern number is odd, a vortex in the gauge field accompanies an ...
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Magnetization Plateau and Entanglement
In some low dimensional quantum spin systems, magnetization plateau is observed before the saturation in magnetization curve. .
I have couple of questions related to this effect-
It seems, ...
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Breaking a classical ground state degeneracy by a quantum term and order-by-disorder
Let’s assume we have a Hamiltonian for spin-1/2 particles with two terms, a classical interaction term and a “quantum” (non-diagonal) term. For simplicity, let’s assume that the quantum term is a ...
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Isotropic classical model with a different phase transition than its anisotropic quantum limit
I have often heard that the isotropic ferromagnetically-coupled 2d classical Ising model and the quantum 1d transverse field Ising model have similar phases and the same universality class of their ...
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Integrability of long range Heisenberg chain
Is the long range heisenberg spin 1/2 chain integrable?
More generally, is the long range version of famous spin chain models integrable?
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Why is my Ising Gauge Theory calculation showing magnetization?
I wrote a Mathematica code to test out the 2d Ising Gauge Theory (by computing the exact partition fucntion) on a $3\times 3$ lattice (so that there are ($4\times 3$ spins on the horizontal bonds and $...
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Ising model and the axiomatics of Statistical Mechanics
I am revisiting Statistical Mechanics to better understand models of spin glass and was wondering to what extent axiomatics of Stat.Mech. applies to an ensamble of spin configurations. In particular, ...
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Equivalent definitions of (dis)continuous phase transitions at criticality
Consider a classical lattice model on $\mathbb{Z}^d$ and suppose that the system undergoes a phase transition as you lower the temperature, i.e., increase $\beta$. The most general definition of a ...
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Two-dimensional Ising model for square lattices
Consider Onsager's exact solution of two-dimensional Ising model for square lattices with nearest neighbour interaction energy ‘J ‘being equal in the horizontal and vertical directions. At the ...
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Obtaining the Ising and XY model from the XYZ $O(3)$ model
I have the classical XYZ model Hamiltonian $\mathcal{H}$ with a magnetic field $\vec{H}$ given as
\begin{equation}
\mathcal{H} =
-\sum_{i< j} J^x_{ij}S_i^xS_{j}^x + J^y_{ij}i^yS_{j}^y+ J^z_{ij}S_z^...
- 904
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Tunneling lowers the energy of a ground state superposition of spins up and down in the quantum Ising model
Considering an Ising model in the quantum scenario in quantum spatial dimension d=1 (that corresponds to classical D=2=d+1 dimension). Starting with the Ising model hamiltonian under the approximation ...
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What is a parent Hamiltonian? [closed]
The term is used throughout the literature but I was not able to find a definition or even a paper properly introducing the term. What does a Hamiltonian have to satisfy to be a parent Hamiltonian?
An ...
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How to show random cluster models with non-integer $q$ have no local description?
It is known that the random cluster model with $q = 1$ corresponds to bond percolation, and $q = 2, 3, ... $ corresponds to the $q$-state Potts model. Both of these have a local description.
What ...
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Spin lattice model fitting particular spin correlations and spectra
I want to write down a spin hamiltonian for $N$ sites (let's say for starters each site is spin = 1/2) that yields particular spin correlation functions,
$$C_{ij} = \langle \hat{\vec{S}}_{i} \cdot \...
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