# Questions tagged [lattice-model]

Lattice is a way of discretizing a quantum field theory for numerical simulations.

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### Velocity driven Poiseuille flow using the incompressible lattice Boltzmann method

My goal here is to develop a Poiseuille flow in a channel, using constant pressure and zero velocity as initial conditions. From what I have read, people seem to be mostly using pressure-driven, or ...
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### What is the lattice temperature?

I am wondering how the lattice temperature is defined in this context. Is it the temperature on which the energy is big enough to split the crystal in it's components (atoms)?
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### Find tools to better understand crystal structure

I am currently studying solid state physics. But I have trouble understanding the crystal structure (or lattice structure), such as the structure in this picture (just to give an example). When I look ...
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### Can someone tell what are primitive translation vectors for BCC lattice?

I referred internet and two very renowned books ( Puri-Babbar and SO PILLAI ). COULDN'T find any primitive translation vector explanation for BCC or FCC. Eventually when I moved on to Reciprocal ...
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### What do the points in the reciprocal lattice stand for?

I'm wondering for what the points in the reciprocal lattice physically stand for, I know that they are the k-vectors, that are the fourier-transformed vectors of the lattice in the real space. Do ...
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### Ising model operators

Ising model formulated as lattice theory with local degrees of freedom described by $s_i$ $i\in 1, \dots, N$ and energy: $$E[\sigma_i] = -J\sum_{<ij>} s_i s_j$$ From $s_i$ I can construct a ...
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### Phase diagram of ${\rm O}(3)$ lattice model and mean field theory

In David Tong: Lectures on Statistical Field Theory Problem Sheet 1 exist task: I fully understand this problem and I know solution: section 17.2. I am interested in application of mean field theory ...
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### Symmetries in the Hubbard model

I would like to understand both in an intuive and in a mathematical way the meaning of the sentence "The Hubbard Hamiltonian has an SU(2) symmetry". What are the symmetry transformations that leave ...
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### Partition function of 2D Ising model on a squared lattice in the canonical ensemble in the low temperature limit

I'm currently working through David Tong's script on statistical mechanics (http://www.damtp.cam.ac.uk/user/tong/statphys/sp.pdf) and came across something that I don't quite understand (page 166). ...
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### Initial conditions in incompressible lattice Boltzmann method

I have very recently come to LB methods, and, after some reading, have implemented a little 2D code of my own. It uses some of the most basic assumptions : D2Q9 lattice BGK collision operator Zou-He ...
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### Do all the classical critical lattice models have emergent conformal invariance?

I understand that any quantum lattice model at the critical point which can be described by a massless relativistic quantum field theory has emergent conformal invariance. My question is what about ...
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### Are all lengths multiples of the Planck length? [duplicate]

If the Planck length is the smallest unit of length that has any physical meaning then is it true to think that all the lengths are multiple of the Planck length?
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### Geometrical proof of number of lattice points in 3D lattice

It is well known that number of lattice points in three-dimensional (3D) objects of simple cubic lattice, body-centered cubic lattice, and face-centered cubic lattice are 1, 2, and 4, respectively (...
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### The frame of truncated momentum basis on a 1D lattice

$\def\ket#1{\left|#1\right\rangle } \def\bra#1{\left\langle #1\right|}$ (This is part of a research problem) The Setup: Consider a single particle on a finite 1D lattice with the Hilbert space ...
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### Is QCD computable?

Are arbitrarily good approximations of the time evolution of any QCD system, given initial and boundary conditions, Turing computable? Can lattice QCD simulations be used to do so in theory? How ...
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### Is is cheating to use alpha strong (instead of V_QCD) to argue that there is asymptotic freedom of QCD?

For asymptotic freedom of QCD, people give the argument that alpha_strong decreases at high energy (thus there is freedom at low distance). But if we make the reasoning on the QCD potential, for ...
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### Is the QCD potential really monotonic ? How does it prevent two quarks from meson to annihilate?

The QCD potential is made of two terms -(4/3) * alpha_s / r that describes the short distance and the term +k*r that describes the long distance Of course, alpha is a function of energy, so it is ...
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### Quantum Monte Carlo Loop Algorithm for quantum spin: why is the freezing graph present in ferromagnetic Ising model?

I study the loop algorithm (Evertz et al). I cannot understand, why the freezing graph type where we have to flip all 4 spins together is not present for the quantum-XY model and the anti-/...
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