ISSN:
1572-9613
Keywords:
Kac potential
;
mean-field theory
;
variational principle
;
helicoidal phase
;
crossover
;
Lifshitz point
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract We consider an Ising model with Kac potential γdK(γ¦x¦) which may have arbitrary sign, and show, following Gates and Penrose, that the free energy in the classical limitγ→0+ can be obtained from a variational principle. When the Fourier transform of the potential has its maximum atp=0 one recovers the usual mean-field theory of magnetism. When the maximum occurs forp 0≠0, however, one obtains an oscillatory or helicoidal phase in which the magnetization near the critical point oscillates with period 2π/¦p 0¦. An example with a potential possessing parameter-dependent oscillations is shown to exhibit crossover phenomena and a multicritical Lifshitz point in the classical limit.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01011152
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