2,083 research outputs found
Information Geometry and Phase Transitions
The introduction of a metric onto the space of parameters in models in
Statistical Mechanics and beyond gives an alternative perspective on their
phase structure. In such a geometrization, the scalar curvature, R, plays a
central role. A non-interacting model has a flat geometry (R=0), while R
diverges at the critical point of an interacting one. Here, the information
geometry is studied for a number of solvable statistical-mechanical models.Comment: 6 pages with 1 figur
Fat and Thin Fisher Zeroes
We show that it is possible to determine the locus of Fisher zeroes in the
thermodynamic limit for the Ising model on planar (``fat'') phi4 random graphs
and their dual quadrangulations by matching up the real part of the high- and
low-temperature branches of the expression for the free energy. Similar methods
work for the mean-field model on generic, ``thin'' graphs. Series expansions
are very easy to obtain for such random graph Ising models.Comment: 3 pages, LaTeX, Lattice2001(surfaces
Frustrating and Diluting Dynamical Lattice Ising Spins
We investigate what happens to the third order ferromagnetic phase transition
displayed by the Ising model on various dynamical planar lattices (ie coupled
to 2D quantum gravity) when we introduce annealed bond disorder in the form of
either antiferromagnetic couplings or null couplings. We also look at the
effect of such disordering for the Ising model on general and
Feynman diagrams.Comment: 7pages, LaTex , LPTHE-ORSAY-94-5
Numerical studies of the two- and three-dimensional gauge glass at low temperature
We present results from Monte Carlo simulations of the two- and
three-dimensional gauge glass at low temperature using the parallel tempering
Monte Carlo method. Our results in two dimensions strongly support the
transition being at T_c=0. A finite-size scaling analysis, which works well
only for the larger sizes and lower temperatures, gives the stiffness exponent
theta = -0.39 +/- 0.03. In three dimensions we find theta = 0.27 +/- 0.01,
compatible with recent results from domain wall renormalization group studies.Comment: 7 pages, 10 figures, submitted to PR
Marginal Pinning of Quenched Random Polymers
An elastic string embedded in 3D space and subject to a short-range
correlated random potential exhibits marginal pinning at high temperatures,
with the pinning length becoming exponentially sensitive to
temperature. Using a functional renormalization group (FRG) approach we find
, with the
depinning temperature. A slow decay of disorder correlations as it appears in
the problem of flux line pinning in superconductors modifies this result, .Comment: 4 pages, RevTeX, 1 figure inserte
A microscopic approach to critical phenomena at interfaces: an application to complete wetting in the Ising model
We study how the formalism of the Hierarchical Reference Theory (HRT) can be
extended to inhomogeneous systems. HRT is a liquid state theory which
implements the basic ideas of Wilson momentum shell renormalization group (RG)
to microscopic Hamiltonians. In the case of homogeneous systems, HRT provides
accurate results even in the critical region, where it reproduces scaling and
non-classical critical exponents. We applied the HRT to study wetting critical
phenomena in a planar geometry. Our formalism avoids the explicit definition of
effective surface Hamiltonians but leads, close to the wetting transition, to
the same renormalization group equation already studied by RG techiques.
However, HRT also provides information on the non universal quantities because
it does not require any preliminary coarse graining procedure. A simple
approximation to the infinite HRT set of equations is discussed. The HRT
evolution equation for the surface free energy is numerically integrated in a
semi-infinite three-dimensional Ising model and the complete wetting phase
transition is analyzed. A renormalization of the adsorption critical amplitude
and of the wetting parameter is observed. Our results are compared to available
Monte Carlo simulations.Comment: To be published in Phy. Rev.
Velocity-force characteristics of a driven interface in a disordered medium
Using a dynamic functional renormalization group treatment of driven elastic
interfaces in a disordered medium, we investigate several aspects of the
creep-type motion induced by external forces below the depinning threshold
: i) We show that in the experimentally important regime of forces
slightly below the velocity obeys an Arrhenius-type law
with an effective energy barrier
vanishing linearly when f approaches the threshold . ii) Thermal
fluctuations soften the pinning landscape at high temperatures. Determining the
corresponding velocity-force characteristics at low driving forces for internal
dimensions d=1,2 (strings and interfaces) we find a particular non-Arrhenius
type creep involving the reduced threshold
force alone. For d=3 we obtain a similar v-f characteristic which is,
however, non-universal and depends explicitly on the microscopic cutoff.Comment: 9 pages, RevTeX, 3 postscript figure
The three-dimensional random field Ising magnet: interfaces, scaling, and the nature of states
The nature of the zero temperature ordering transition in the 3D Gaussian
random field Ising magnet is studied numerically, aided by scaling analyses. In
the ferromagnetic phase the scaling of the roughness of the domain walls,
, is consistent with the theoretical prediction .
As the randomness is increased through the transition, the probability
distribution of the interfacial tension of domain walls scales as for a single
second order transition. At the critical point, the fractal dimensions of
domain walls and the fractal dimension of the outer surface of spin clusters
are investigated: there are at least two distinct physically important fractal
dimensions. These dimensions are argued to be related to combinations of the
energy scaling exponent, , which determines the violation of
hyperscaling, the correlation length exponent , and the magnetization
exponent . The value is derived from the
magnetization: this estimate is supported by the study of the spin cluster size
distribution at criticality. The variation of configurations in the interior of
a sample with boundary conditions is consistent with the hypothesis that there
is a single transition separating the disordered phase with one ground state
from the ordered phase with two ground states. The array of results are shown
to be consistent with a scaling picture and a geometric description of the
influence of boundary conditions on the spins. The details of the algorithm
used and its implementation are also described.Comment: 32 pp., 2 columns, 32 figure
New Criticality of 1D Fermions
One-dimensional massive quantum particles (or 1+1-dimensional random walks)
with short-ranged multi-particle interactions are studied by exact
renormalization group methods. With repulsive pair forces, such particles are
known to scale as free fermions. With finite -body forces (m = 3,4,...), a
critical instability is found, indicating the transition to a fermionic bound
state. These unbinding transitions represent new universality classes of
interacting fermions relevant to polymer and membrane systems. Implications for
massless fermions, e.g. in the Hubbard model, are also noted. (to appear in
Phys. Rev. Lett.)Comment: 10 pages (latex), with 2 figures (not included
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