Spin-1 triangular lattice Ising model: Consider a ferromagnetic spin-1 triangular lattice Ising model. The Hamiltonian is H=-J sum_((:ij:)) S_(i)^(z)S_(j)^(z)-H sum_i S_(i)^(z) where S_(i)^(z)in{-1,0,+1} on each site i,H is a uniform magnetic field, and where the first sum is over all links of the lattice. (a) Derive the mean field Hamiltonian H_(M

Question

Spin-1 triangular lattice Ising model: Consider a ferromagnetic spin-1 triangular lattice Ising model. The Hamiltonian is

H=-J\sum_((:ij:)) S_(i)^(z)S_(j)^(z)-H\sum_i S_(i)^(z)

where

S_(i)^(z)in{-1,0,+1}

on each site

i,H

is a uniform magnetic field, and where the first sum is over all links of the lattice. (a) Derive the mean field Hamiltonian

H_(MF)

for this model. (b) Derive the free energy per site

f_(MF)

within the mean field approach. (c) Derive the self-consistent equation for the local magnetization

m=(:S_(i)^(z):)

, and find the critical temperature

T_(c)(H

)

=

(

0)

. (d) Expand the mean field free energy as

f(m,h)=f_(0)+(t)/(2)m^(2)+um^(4)-hm+O(h^(2),hm^(3),m^(6))

Find

f_(0),t,u

, and

h

in terms of

J,H

, and

k_(B)T

.

Accepted Answer

Expert Answer to - Spin-1 triangular lattice Ising model: Consider a ferromagnetic spin-1 triangular lattice Ising mode

Answer

Solution for - Spin-1 triangular lattice Ising model: Consider a ferromagnetic spin-1 triangular lattice Ising mode

Answer

This an additional answer to - Spin-1 triangular lattice Ising model: Consider a ferromagnetic spin-1 triangular lattice Ising mode

(Solved): Spin-1 triangular lattice Ising model: Consider a ferromagnetic spin-1 triangular lattice Ising mode ...