148 research outputs found
Revisiting the field-driven edge transition of the tricritical two-dimensional Blume-Capel model
We reconsider the tricritical Blume-Capel model on the square lattice with a magnetic field acting on the open boundaries in one direction. Periodic boundary conditions are applied in the other direction. We apply three types of Monte Carlo algorithms, local Metropolis updates, and cluster algorithms of the Wolff and geometric type, adapted to the symmetry properties of the model. Statistical analyses of the bulk magnetization, the bulk Binder ratio, the edge magnetization, and the connected product of the edge and bulk magnetizations lead to new results confirming the presence of a singular edge transition at Hsc≈0.68, as we reported earlier [Phys. Rev. E 71, 026109 (2005)]. We provide a plausible answer concerning a discrepancy between the behavior of the edge Binder ratio reported in that work and our new results.Theoretical Physic
Symmetries, Horizons, and Black Hole Entropy
Black holes behave as thermodynamic systems, and a central task of any
quantum theory of gravity is to explain these thermal properties. A statistical
mechanical description of black hole entropy once seemed remote, but today we
suffer an embarrassment of riches: despite counting very different states, many
inequivalent approaches to quantum gravity obtain identical results. Such
``universality'' may reflect an underlying two-dimensional conformal symmetry
near the horizon, which can be powerful enough to control the thermal
characteristics independent of other details of the theory. This picture
suggests an elegant description of the relevant degrees of freedom as
Goldstone-boson-like excitations arising from symmetry breaking by the
conformal anomaly.Comment: 6 pages; first prize essay, 2007 Gravity Research Foundation essay
contes
Medium-range percolation in two dimensions
We investigate equivalent-neighbor percolation models in two dimensions with a variable interaction range, and include the mean-field limit. We employ a Monte Carlo algorithm whose efficiency depends only weakly on the number of equivalent neighbors within the range of the interactions. We consider 2 classes of models, one in which the interacting neighbors fill a circle, and one in which they fill a square. We first determine the critical points, and then determine the critical exponents. These are, for all finite ranges investigated, in agreement with the exactly known exponents of the nearest-neighbor model.Theoretical Physic
Completely packed O(n) loop models and their relation with exactly solved coloring models.
Theoretical Physic
The triangular Ising antiferromagnet in a staggered field
We study the equilibrium properties of the nearest-neighbor Ising
antiferromagnet on a triangular lattice in the presence of a staggered field
conjugate to one of the degenerate ground states. Using a mapping of the ground
states of the model without the staggered field to dimer coverings on the dual
lattice, we classify the ground states into sectors specified by the number of
``strings''. We show that the effect of the staggered field is to generate
long-range interactions between strings. In the limiting case of the
antiferromagnetic coupling constant J becoming infinitely large, we prove the
existence of a phase transition in this system and obtain a finite lower bound
for the transition temperature. For finite J, we study the equilibrium
properties of the system using Monte Carlo simulations with three different
dynamics. We find that in all the three cases, equilibration times for low
field values increase rapidly with system size at low temperatures. Due to this
difficulty in equilibrating sufficiently large systems at low temperatures, our
finite-size scaling analysis of the numerical results does not permit a
definite conclusion about the existence of a phase transition for finite values
of J. A surprising feature in the system is the fact that unlike usual glassy
systems, a zero-temperature quench almost always leads to the ground state,
while a slow cooling does not.Comment: 12 pages, 18 figures: To appear in Phys. Rev.
Transfer-Matrix Monte Carlo Estimates of Critical Points in the Simple Cubic Ising, Planar and Heisenberg Models
The principle and the efficiency of the Monte Carlo transfer-matrix algorithm
are discussed. Enhancements of this algorithm are illustrated by applications
to several phase transitions in lattice spin models. We demonstrate how the
statistical noise can be reduced considerably by a similarity transformation of
the transfer matrix using a variational estimate of its leading eigenvector, in
analogy with a common practice in various quantum Monte Carlo techniques. Here
we take the two-dimensional coupled -Ising model as an example.
Furthermore, we calculate interface free energies of finite three-dimensional
O() models, for the three cases , 2 and 3. Application of finite-size
scaling to the numerical results yields estimates of the critical points of
these three models. The statistical precision of the estimates is satisfactory
for the modest amount of computer time spent
Equilibrium crystal shapes in the Potts model
The three-dimensional -state Potts model, forced into coexistence by
fixing the density of one state, is studied for , 3, 4, and 6. As a
function of temperature and number of states, we studied the resulting
equilibrium droplet shapes. A theoretical discussion is given of the interface
properties at large values of . We found a roughening transition for each of
the numbers of states we studied, at temperatures that decrease with increasing
, but increase when measured as a fraction of the melting temperature. We
also found equilibrium shapes closely approaching a sphere near the melting
point, even though the three-dimensional Potts model with three or more states
does not have a phase transition with a diverging length scale at the melting
point.Comment: 6 pages, 3 figures, submitted to PR
Three-dimensional Ising model in the fixed-magnetization ensemble: a Monte Carlo study
We study the three-dimensional Ising model at the critical point in the
fixed-magnetization ensemble, by means of the recently developed geometric
cluster Monte Carlo algorithm. We define a magnetic-field-like quantity in
terms of microscopic spin-up and spin-down probabilities in a given
configuration of neighbors. In the thermodynamic limit, the relation between
this field and the magnetization reduces to the canonical relation M(h).
However, for finite systems, the relation is different. We establish a close
connection between this relation and the probability distribution of the
magnetization of a finite-size system in the canonical ensemble.Comment: 8 pages, 2 Postscript figures, uses RevTe
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