For example you have spin ##S=\frac{7}{2}## and for example ##J=10## quantum Heisenberg model. And you have Monte Carlo simulation code for classical Heisenberg ##S=\infty##. What should you use for ##J## in classical Heisenberg model Monte Carlo code?
I'm speaking in general. I just see that in some papers some authors uses for example four sublattices for body centered cubic lattice. Why not two? I don't understand this.
In ordinary definition antiferromagnet lattice has to sublattices, one with spins up, and one with of spin down in ##T=0##. Why in some cases people discuss situations with four or even more subblatices? Do you have explanation for this? Some references maybe?
In quantum Heisenberg model
\hat{H}=-J\sum_{\vec{n},\vec{m}}\hat{\vec{S}}_{\vec{n}}\cdot \hat{\vec{S}}_{\vec{m}}
##J## can be obtained from dispersion experiment. For large spin ##S## even classical Heisenberg model is good for description of Curie temperature for example. Is that with the same...
What is refered as one Monte Carlo step. In all books, papers people is written that was performed ##5 \cdot 10^{6}## MCS on all system sizes. Or the time is measured in MCS. But what is refered as one MCS? For example in MC simulation of Ising model what is a one MCS?
Zero field magnetisation like a function of temperature vanished in ##T=T_c## as ##(T_c-T)^{\beta}##. Let ##M_1## be a magnetisation for temperature ##T_1##. Since ##\forall M<M_1##, ##(\frac{\partial A}{\partial M})_T=H=0## it follows that
A(T_1,M)=A(T_1,0) for ##M \leq M_1(T_1)##
Why only for...
Because I still didn't find answer for my question I will write here more details.
So ##G(T,H)## is Gibbs thermodynamics potential. Derivatives of Gibbs potential are defined by
(\frac{\partial G}{\partial H})_T \equiv G^{(1)}\propto (1-\frac{T}{T_c})^{-\Delta'_1}G^{(0)}
(\frac{\partial...
I think that this is very hard problem, and not precise theory.
Helmholtz potential is convex function of magnetisation.
A(T,M)=\sum^{\infty}_{j=0}L_j(T)M^j
that must put some demands on coefficients in series, and if I say
L_j(T)=l_{j0}+l_{j1}(T-T_c)+...
I have a problem with...
Assume that we can expand the Helmholtz potential about T=T_c, M=0 in a standard Taylor series form of functions of the variables,
A(T,M)=\sum^{\infty}_{j=0}L_j(T)M^j=L_0(T)+L_2(T)M^2+L_4(T)M^4+...
Why A(T,M) must be even function of M?
Coefficients can be expanded about T=T_c...
Gap exponents are denoted like critical exponents for higher derivatives of Gibbs potential.
\Delta_l'
(\frac{\partial G}{\partial H})_T=G^{(1)}\propto (1-\frac{T}{T_c})^{-\Delta_1'}G^{0}
(\frac{\partial^l G}{\partial H^l})_T=G^{(1)}\propto (1-\frac{T}{T_c})^{-\Delta_l'}G^{l-1}
\alpha'...
No. You have sum.
So
Spins may take values +1 or -1. Because of that
result of
S_iS_jS_jS_k
is either +1 or -1.
For example
\sum_{S_1=-1,1}\sum_{S_2=-1,1}S_iS_{i+1}=-1 \cdot (-1)+(-1)\cdot 1+1\cdot(-1)+1-1 \cdot (-1)+(-1)\cdot 1+1\cdot(-1)=0
I don't know what that means in the graph...
In book Modern theory of critical phenomena author Shang - Keng Ma in page 17.
\sigma_{\vec{k}}=V^{-\frac{1}{2}}\int d^3\vec{x}e^{-i\vec{k}\cdot\vec{x}}\sigma(\vec{x})
\sigma(\vec{x})=V^{-\frac{1}{2}}\sum_{\vec{k}}e^{i\vec{k}\cdot \vec{x}}\sigma_{\vec{k}}
Is this correct? How can inversion of...
One line between (+-). Two lines between (++). Zero line between (--). \gamma number of nearest neighbours. Why we have relation
\gamma N_+=2N_{++}+N_{+-}
Why we get this? Some explanation. This is from Kerson Huang.
MFA
\hat{A}\hat{B}\approx \hat{A}\langle\hat{B}\rangle+\hat{B}\langle\hat{A}\rangle-\langle\hat{A}\rangle\langle\hat{B}\rangle
What this mean physically? What we neglect here?
If I calculate Neel temperature using this method T_N^{MFA} and using RPA method T_N^{RPA} is there some relation...