Grégory Schehr | PubMed Health

PubMed2006

Strong-disorder fixed point in the dissipative random transverse-field Ising model.

The interplay between disorder, quantum fluctuations, and dissipation is studied in the random transverse Ising chain coupled to a dissipative Ohmic bath with a real space renormalization group. A typically very large length scale L* is identified above which the physics of frozen clusters dominates. Below L* a strong-disorder fixed point determines scaling at a pseudocritical point. In a Griffiths-McCoy region frozen clusters produce already a finite magnetization resulting in a classical low temperature behavior of the susceptibility and specific heat. These override the confluent singularities that are characterized by a continuously varying exponent z and are visible above a temperature T*approximately L*-z.

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PubMed2006

Universal asymptotic statistics of maximal relative height in one-dimensional solid-on-solid models.

We study the probability density function P(h(m), L) of the maximum relative height h(m) in a wide class of one-dimensional solid-on-solid models of finite size L. For all these lattice models, in the large-L limit, a central limit argument shows that, for periodic boundary conditions, P(h(m), L) takes a universal scaling form P(h(m), L) approximately radical(12w(L))(-1) f(h(m)radical(12w(L))(-1), with w(L) the width of the fluctuating interface f(x) and the Airy distribution function. For one instance of these models, corresponding to the extremely anisotropic Ising model in two dimensions, this result is obtained by an exact computation using the transfer matrix technique, valid for any L > 0. These arguments and exact analytical calculations are supported by numerical simulations, which show in addition that the subleading scaling function is also universal, up to a nonuniversal amplitude, and simply given by the derivative of the Airy distribution function f'(x).

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