Questions tagged [lattice-model]
Lattice is a way of discretizing a quantum field theory for numerical simulations.
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How to define an effective light cone or null direction from discrete arrival times on a lattice?
In several discrete or lattice-based approaches to spacetime (causal sets, Regge-like discretizations, lattice field theory, numerical GR, fast-marching/eikonal methods), one often works with a ...
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Creutz, "Quarks, Gluons And Lattices", equations (5.31), (5.32). Struggling to prove them [duplicate]
I've realised that this question is a duplicate of Proof involving exponential of anticommuting operators, where one can find some answer.
I'm struggling to show the equations mentionned in the title. ...
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Spacetime as a lattice in classical mechanics
I am currently studying lattice methods to be able to apply them to lattice QCD later. In order to get a good intuition, I deem it adequate to do the following exercise: I would like to formulate the ...
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How to make sense of non-planar Wilson loops on the lattice?
I am operating with a (more or less standard) Metropolis+Overrelaxation algorithm a series of Wilson loops on a $N_t\times N_s^2=48^2\times 16$ (2+1) dimensional Euclidean lattice. I am simulating ...
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Is it possible to analytically continue magnetization in one-dimensional Ising models?
I am asking about the infinitely long layered Ising model with a finite number of layers. The model is assumed to be invariant under translations along the direction in which it is infinite. All ...
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Can the index in the pre-exponential factor in the correlation function depend on the direction?
There is quite a lot of discussion on SE about correlation functions in lattice models. So I would say that it is well known that the two-spin (two-point) correlation function has the following ...
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How to Calculate Virasoro's Characters of Critical 3-state Pott's model without Considering $W$ algebra?
Let's consider the critical 3-state Potts model. According to conformal field theory, it corresponds to a CFT with a central charge $c=\frac{4}{5}$. However, there are 10 characters for $c=\frac{4}{5}$...
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Do the momentum values and the winding numbers in a compactified string theory be periodic too(along with being discrete)?
I have a question. In lattice qcd, we compactify space to make it periodic. Also because of the formation of the reciprocal brilliouin zone, even momentum becomes discrete valued and periodic. Because ...
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Non-doubled semion model?
There exists an abelian (2+1)d unitary topological quantum field theory (TQFT), with a single non-trivial particle: the semion TQFT. However, all microscopic (lattice) models I know of realise the ...
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Literature request about lattice gas with nearest-neighbor interaction
I have a square lattice, in which each cell can be occupied by a molecule or can be empty. This should be a "lattice gas". Then I introduce a nearest-neighbor interaction of energy $h$:
the ...
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Positivity of the determinant of the lattice Dirac operator in (2+1)D on the lattice
As shown in "Gattringer & Lang, Quantum Chromodynamics on the Lattice, sec. 5.4.3" the lattice Dirac operator $D$ for Wilson fermions satisfies the property of "$\gamma_5$-...
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Ising model from the $\varphi^4$ scalar field theory
More than a year ago, I came across a paper (which I am unable to find at the moment) that mentioned the following statement: the Ising model is a discretized version of $\varphi^4$-scalar field ...
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Is Gauss law constraint in gauging a global symmetry on lattice a dynamical constraint or a kinematical constraint?
Suppose a lattice system is $G$-symmetric, when we try to gauge this symmetry, we follow the following steps (for example toric code Levin Gu Xie Chen):
minimal coupling: the original Hamiltonian is ...
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How to Invert Dispersion Relation $\epsilon_k=2t[\cos(k_x a) + \cos(k_y a)]$ to Solve for Wavevectors $k_x$ and $k_y$ in Terms of Energy $\epsilon_k$?
I am working on a problem related to the dispersion relation of electrons in a 2D square lattice with nearest-neighbor hopping. The energy $\epsilon_k$ is given by:
$
\epsilon_k = 2t [\cos(k_x a) + \...
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Using boundary conditions to find periodicity in integrable toda-chain
I've been thinking about the one-dimensional Toda chain which is an integrable system, as a toy-model for a crystal. I'm trying to find methods to find the natural periodicity which should be ...
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Velocity of Wilson fermions
Consider a LFT of Wilson fermions given by $$H=\int \frac{dk}{2\pi}\psi_k^\dagger\left(-\frac{\sin(ka)}{a}\gamma^0\gamma^1+\left(m+\frac{1-\cos(k a)}{a}\right)\gamma^0\right)\psi_k.$$
For given $m$ ...
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Correspondence between the Ising model considering vacancy and lattice gas
Several textbooks discuss the equivalence between the Ising model and the lattice gas. However, I have never seen a textbooks/article that discuss the correspondence between the Ising model with ...
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Field theory based on square-well potential?
Is it possible to find the behavior of a field theory with a square well in the Lagrangian? Usually, we have polynomial terms, and one can argue (see e.g. in [physics SE q41065]) that the simplest ...
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Ising model in a magnetic field (phase transition?)
I have some questions regarding the Ising model in the presence of a magnetic field which is non-uniform.
Let us define the Ising Hamiltonian on a $d-$dimensional lattice,
$$ H = -\frac{1}{2} \sum_{i,...
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Why is Wigner-Seitz cell considered primitive?
During the lecture I listened, as well as in the internet, in Wikipedia for example, unit cell was defined as the parallelepiped spanned by the translation vectors. Primitive cell was defined as the ...
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Non-adiabatic evolution and time-dependent adiabatic parameter
I am dealing with the dynamics of a two-bands lattice system. The idea is that you have a lattice model of free fermions, with some hopping amplitudes and on-site energies.The lattice have two fermion ...
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The 2d Ising transfer matrix and the effect of anisotropy on more general transfer matrices
The 2d Ising model has a row-to-row transfer matrix that can be written suggestively as
$$T = e^{\tau \sum_i \sigma^z_i \sigma^z_{i+1}} e^{ \lambda \tau \sum_i \sigma^x_i}$$
where $\tau$ and $\lambda$ ...
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Intuition for ground state degeneracy of Majorana checkerboard model
I'm now trying to learn about Fracton. In the very early paper studying Majorana checkerboard model, it is claimed that the ground state degeneracy ${D_0}$ on ${L \times L \times L}$ 3-torus is ${...
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Why each normal mode is treated as a harmonic oscillator in Debye's calculation of specific heat?
So in Einstein's calculation of specific heat each oscillator is assumed to be vibrating with same frequency and its average energy is given by hv(n+1/2) where n is bose factor. Debye said that ...
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Phase transition in Ising Model with local $\mathbb{Z}_2$ symmetry
I am studying the Ising model with a local $\mathbb{Z}_2$ gauge symmetry
\begin{equation}
\mathcal{H} = -\sum_{\text{plaquettes}} \sigma^z(\vec{x}, \vec{\mu})\sigma^z(\vec{x}+\vec{\mu}, \vec{\nu})\...
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