A mathematical model used in physics primarily to explain magnetism.
Questions tagged [spin-models]
471 questions
27
votes
1 answer
Mermin-Wagner theorem in the presence of hard-core interactions
It seems quite common in the theoretical physics literature to see applications of the "Mermin-Wagner theorem" (see wikipedia or scholarpedia for some limited background) to systems with hard-core interactions; for example to conclude that genuine…
Yvan Velenik
- 11,352
24
votes
1 answer
Fluctuations of an interface with hammock potential
This question is related to that one. I ask it here since comments are too short for the extended discussion that was going on there.
I am interested in a very simple interface model. To each $x\in\mathbb{Z}^2$, we associate a random height…
Yvan Velenik
- 11,352
22
votes
2 answers
What new features does the Heisenberg Model have compared to the Ising Model?
Both the Ising and the Heisenberg Models describe spin lattices with interaction on first neighbors. The Hamiltonian in each case is quite similar, despite the fact of treating de spins as Ising variables (1 or -1) or as quantum operators. In the…
P. C. Spaniel
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19
votes
2 answers
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:
$$
H = \frac{\Delta}{2}\sum_i \Pi^2_i - \sum_{i
derpy
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17
votes
1 answer
Phase Transition in the Ising Model with Non-Uniform Magnetic Field
Consider the Ferromagnetic Ising Model ($J>0$) on the lattice $\mathbb{Z}^2$ with the Hamiltonian with boundary condition $\omega\in\{-1,1\}$ formally given by
$$
H^{\omega}_{\Lambda}(\sigma)=-J\sum_{}{\sigma_i\sigma_j} - \sum_{i\in\Lambda}…
Leandro
17
votes
1 answer
Examples of Matrix Product States
Matrix product states (MPS) are a way of representing a (many-body) wavefunction. The method has been described, for example, in
The density-matrix renormalization group in the age of matrix product states. U. Schollwoeck. Ann. Phys 326, 96 (2011),…
adhip agarwala
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15
votes
1 answer
What is the difference between spin glass and spin liquid?
What is the difference between spin glass and spin liquid?
Do they both originate from frustration?
user16064
13
votes
3 answers
Visualization of 1D spin chain wave fuction
What are the known methods for visualizing quantum states of one-dimensional spin chains? They can be based either on their wave functions or density matrices.
My particular interest is in plotting eigenstates of 1D spin chains (e.g. Heisenberg…
Piotr Migdal
- 6,530
12
votes
2 answers
What is the intuition behind the statement that non-equilibrium systems with static disorder are self-averaging?
In this paper(1) by C. De Dominics, he makes the argument that in a dynamical statistical mechanics system, one doesn't need to apply the replica trick and can directly disorder average the generating function $$\bar Z[j] = \langle Z[j]…
Adam B
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12
votes
1 answer
Kosterlitz-Thouless in the XXZ chain: instanton condensation?
The anisotropic spin-$\frac{1}{2}$ Heisenberg chain $$H = \sum_n S^x_n S^x_{n+1} + S^y_n S^y_{n+1} + \Delta S^z_n S^z_{n+1}$$ is known to have the same physics as the two-dimensional classical XY model. More concretely, at $\Delta = 1$ it undergoes…
Ruben Verresen
- 9,713
12
votes
2 answers
Goldstone's theorem, symmetry breaking and the Heisenberg model
I'm currently researching symmetry breaking and Goldstone's theorem for a project in my third year of my theoretical physics degree. So my knowledge isn't from a formal teaching but my own research.
I began with trying to understand Goldstone's…
Horro
- 143
12
votes
1 answer
What is the difference between classical and quantum Ising model?
The Ising model is defined with the Hamiltonian:
$$
H = -\sum_{}S_i^z\cdot S_j^z
$$
What is the difference between quantum version and classical version? My intuition is that the classical version is equal to quantum version in any dimension…
an offer can't refuse
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11
votes
2 answers
Definition for Chiral Spin Liquid
What is the definition of chiral spin liquid?
Especially what does chiral mean here?
I encounter a lot of terminologies with chiral. It seems they mean differently in different contexts. If you could generally answer what chiral means, it would be…
hehuan0430
- 749
10
votes
1 answer
Is there an entropy crisis in Spin Glasses?
If you cool a material and avoid crystallization, you get a supercooled liquid and ultimately a glass. If you extrapolate the entropy of the supercooled liquid, at some point it intersects with the entropy of the crystal. This is known as the…
9
votes
2 answers
Is the phenomenon of geometrical frustration in condensed matter physics related to some kind of topological invariant?
Edit (attempt to clarify my question a little bit):
I’m not thinking geometrical frustration should be necessarily associated to a topological invariant in a direct way, but maybe local geometrical frustration behaviour correlates to one globally,…
dahemar
- 2,513