Lattice models Definition and 11 Threads

Hello, I am interested in the following model: $$ H = \sum_{<i,j>} -t (c_i c_j^{\dagger} + \text{H.C.}) + U (n_i n_j) + \sum_{<<i,j>>} -t' (c_i c_j^{\dagger} + \text{H.C.}) + U' (n_i n_j) $$ where \( <i,j> \) indicates nearest neighbors, and \( <<i,j>> \) indicates next-nearest neighbors...

LBM model for phase change- relevant equations found here. Also here. #Thermal LBM #solves 1D 1 phase phase-change #D2Q5 Lattice nx=100 # the number of nodes in x direction lattice direction ny=5 # the number of nodes in y...

Hi Pfs Rovelli defines spin networks in this paper https://arxiv.org/abs/1004.1780 for a trivalent node Vn = 0 (the volume) nodes begin to "get" volume with the four valent case. take a cube or a tetrahedron, each vertex is linkes to 3 nodes so they would have a null volume. things are...

Hi Pfs i am interested in spin networks (a pecular lattices) and i found two ways to define them. they both take G = SU(2) as the Lie group. in the both ways the L oriented edges are colored with G representations (elements of G^L the difference is about the N nodes. 1) in the first way the...

Hello. I am looking to learn about averaging out a particle gas or any other type of organization of particles within a system or volume that can be approximated onto a grid or mesh where the particles are at a constant distance from each other: https://en.wikipedia.org/wiki/Particle_mesh. I...

I recently watched this video by David Tong on computer simulation of quantum fields on lattices, fermionic fields in particular. He said it was impossible to simulate a fermionic field on a lattice so that the action be local, Hermitian and translation-invariant unless extra fermions get...

I was reading about numerical methods in statistical physics, and some examples got me thinking about what seems to be combinatorics, an area of math I hardly understand at all beyond the very basics. In particular, I was thinking about how one would go about directly summing the partition...

Hi, I know that the ground state of the spin-1/2 Ising model is the ordered phase (either all spin up or all spin down). But how do I actually go about deriving this from say the one-dimensional spin hamiltonian itself, without having to solve system i.e. finding the partition function? $$...

I've been struggling with a somewhat-recent paper by Charles Francis, "A construction of full QED using finite dimensional Hilbert space," available here: https://arxiv.org/pdf/gr-qc/0605127.pdf But also published in...

I am trying to understand Aubry-Andre model. It has the following form $$H=∑_n c^†_nc_{n+1}+H.C.+V∑_n cos(2πβn)c^†_nc_n$$ This reference (at the 3rd page) says that if ##\beta## is irrational (rational) then the period of potential is quasi-periodic incommensurate (periodic commensurate) with...

Could anyone suggest a book for studying lattice models. Especially xy and Heisenberg models.