科研之友
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摘要
We consider various random models ( directed polymer, ferromagnetic random Potts model, Ising spin glasses) in their disorder-dominated phases, where the free-energy cost F( L) of an excitation of length L presents fluctuations that grow as a power law Delta F( L) similar to L(omega) with the so-called droplet exponent omega > 0. We study the tails of the probability distribution Pi( x) of the rescaled free-energy cost x = (F(L) - (F(L)) over bar)/L(omega), which are governed by two exponents (eta(-),eta(+)) defined by ln Pi(x -> +/-infinity) similar to -|x|(eta +/-). The aim of this paper is to establish simple relations between these tail exponents (eta(-),eta(+)) and the droplet exponent.. We first prove these relations for disordered models on diamond hierarchical lattices where exact renormalizations exist for the probability distribution.( x). We then interpret these relations via an analysis of the measure of the rare disorder configurations governing the tails. Our conclusion is that these relations, when expressed in terms of the dimensions of the bulk and of the excitation surface, are actually valid for general lattices.
- 出版日期2008-1
- 单位中国地震局
