# Search results

1. ### Classical and quantum Heisenberg model

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?
2. ### Antiferromagnet more subblatices

One example will be enough...
3. ### Antiferromagnet more subblatices

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.
4. ### Antiferromagnet more subblatices

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?
5. ### Classical and quantum Heisenberg model

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...
6. ### Monte Carlo step

Suppose that problem is MC simulation of 2d Ising model with ##L^2## lattice sites. What is the one time step of that simulation?
7. ### Monte Carlo step

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?
8. ### The Griffiths inequality

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...
9. ### Gap exponents

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...
10. ### Assumptions of Landau theory

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...
11. ### Assumptions of Landau theory

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...
12. ### Gap exponents

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'...
13. ### Spin product of graphs

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...
14. ### Mistake in book?

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...
15. ### Ising model

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.
16. ### The molecular field approximation

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...
17. ### Magnetism dielectric crystals

What is origin of magnetism in dielectric crystals?
18. ### Frustrated magnetics lattices

What is definition of frustrated magnetics lattices?