On equivalent-neighbour, random site models of disordered systems
Tóm tắt
Models of random systems whose Hamiltonian reads
$$H_\Lambda = - \tfrac{1}{2}\sum\limits_{i,j \in \Lambda } {J_{ij} S_i S_j } $$
, where
$$S_i = \pm 1, J_{ij} = \frac{1}{{\# \Lambda }}(J_0 + \bar \xi _i Q\bar \xi _j + \bar L(\bar \xi _i + \bar \xi _j ), \bar \xi _i = (\bar \xi _{i1} ,...,\bar \xi _{in} )$$
andξ
iμ
,μ=1,...,n are independent, identically distributed random variables are discussed.J
ij
are assumed to be symmetric, with respect toJ
0, random variables and also symmetric functions of components of
$$\bar \xi _i $$
. A question of dependence of a phase diagram on a probability distribution of
$$\bar \xi _i $$
is addressed. A class of distributions and interactionsJ
ij
, which give rise to phase diagrams called typical is selected. Then a problem of obtaining typical phase diagrams, containing a certain region with an infinite number of pure phases, is studied.
Tài liệu tham khảo
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It is obvious that in order to compare models with the same functione but different probability distributions, one has to avoid trivial rescalings by requiring some normalization, for instance that varianceE(ξ 2 i =1(E(ξ i ). Thenq max≦1, sinceE 2(ξ i |)≦E(ξ 0 i
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