29 research outputs found
Topology of event distribution as a generalized definition of phase transitions in finite systems
We propose a definition of phase transitions in finite systems based on
topology anomalies of the event distribution in the space of observations. This
generalizes all the definitions based on the curvature anomalies of
thermodynamical potentials and provides a natural definition of order
parameters. The proposed definition is directly operational from the
experimental point of view. It allows to study phase transitions in Gibbs
equilibria as well as in other ensembles such as the Tsallis ensemble.Comment: 4 pages, 3 figure
Statistical Mechanics in the Extended Gaussian Ensemble
The extended gaussian ensemble (EGE) is introduced as a generalization of the
canonical ensemble. The new ensemble is a further extension of the Gaussian
ensemble introduced by J. H. Hetherington [J. Low Temp. Phys. {\bf 66}, 145
(1987)]. The statistical mechanical formalism is derived both from the analysis
of the system attached to a finite reservoir and from the Maximum Statistical
Entropy Principle. The probability of each microstate depends on two parameters
and which allow to fix, independently, the mean energy of the
system and the energy fluctuations respectively. We establish the Legendre
transform structure for the generalized thermodynamic potential and propose a
stability criterion. We also compare the EGE probability distribution with the
-exponential distribution. As an example, an application to a system with
few independent spins is presented.Comment: Revtex 4, 8 pages, 8 figure
Comment on "Critical properties of highly frustrated pyrochlore antiferromagnets"
We argue that the analysis of Reimers {\it et al.} [ Phys. Rev. B {\bf 45},
7295 (1992)] of their Monte Carlo data on the Heisenberg pyrochlore
antiferromagnet, which suggests a new universality class, is not conclusive. By
re-analysis of their data, we demonstrate asymptotic volume dependence in some
thermodynamic quantities, which suggests the possibility that the transition
may be first order.Comment: 5 pages (RevTex 3.0), 3 figures available upon request, CRPS-93-0
On the inequivalence of statistical ensembles
We investigate the relation between various statistical ensembles of finite
systems. If ensembles differ at the level of fluctuations of the order
parameter, we show that the equations of states can present major differences.
A sufficient condition for this inequivalence to survive at the thermodynamical
limit is worked out. If energy consists in a kinetic and a potential part, the
microcanonical ensemble does not converge towards the canonical ensemble when
the partial heat capacities per particle fulfill the relation
.Comment: 4 pages, 4 figure
Extended gaussian ensemble solution and tricritical points of a system with long-range interactions
The gaussian ensemble and its extended version theoretically play the
important role of interpolating ensembles between the microcanonical and the
canonical ensembles. Here, the thermodynamic properties yielded by the extended
gaussian ensemble (EGE) for the Blume-Capel (BC) model with infinite-range
interactions are analyzed. This model presents different predictions for the
first-order phase transition line according to the microcanonical and canonical
ensembles. From the EGE approach, we explicitly work out the analytical
microcanonical solution. Moreover, the general EGE solution allows one to
illustrate in details how the stable microcanonical states are continuously
recovered as the gaussian parameter is increased. We found out that it
is not necessary to take the theoretically expected limit
to recover the microcanonical states in the region between the canonical and
microcanonical tricritical points of the phase diagram. By analyzing the
entropy as a function of the magnetization we realize the existence of
unaccessible magnetic states as the energy is lowered, leading to a treaking of
ergodicity.Comment: 8 pages, 5 eps figures. Title modified, sections rewritten,
tricritical point calculations added. To appear in EPJ
Scaling laws for the 2d 8-state Potts model with Fixed Boundary Conditions
We study the effects of frozen boundaries in a Monte Carlo simulation near a
first order phase transition. Recent theoretical analysis of the dynamics of
first order phase transitions has enabled to state the scaling laws governing
the critical regime of the transition. We check these new scaling laws
performing a Monte Carlo simulation of the 2d, 8-state spin Potts model. In
particular, our results support a pseudo-critical beta finite-size scaling of
the form beta(infinity) + a/L + b/L^2, instead of beta(infinity) + c/L^d +
d/L^{2d}. Moreover, our value for the latent heat is 0.294(11), which does not
coincide with the latent heat analytically derived for the same model if
periodic boundary conditions are assumed, which is 0.486358...Comment: 10 pages, 3 postscript figure
Magnetic Phase Diagram of the Ferromagnetically Stacked Triangular XY Antiferromagnet: A Finite-Size Scaling Study
Histogram Monte-Carlo simulation results are presented for the magnetic-field
-- temperature phase diagram of the XY model on a stacked triangular lattice
with antiferromagnetic intraplane and ferromagnetic interplane interactions.
Finite-size scaling results at the various transition boundaries are consistent
with expectations based on symmetry arguments. Although a molecular-field
treatment of the Hamiltonian fails to reproduce the correct structure for the
phase diagram, it is demonstrated that a phenomenological Landau-type
free-energy model contains all the esstential features. These results serve to
complement and extend our earlier work [Phys. Rev. B {\bf 48}, 3840 (1993)].Comment: 5 pages (RevTex 3.0), 6 figures available upon request, CRPS 93-
Histogram Monte Carlo study of next-nearest-neighbor Ising antiferromagnet on a stacked triangular lattice
Critical properties of the Ising model on a stacked triangular lattice, with
antiferromagnetic first and second-neighbor in-plane interactions, are studied
by extensive histogram Monte Carlo simulations. The results, in conjunction
with the recently determined phase diagram, strongly suggest that the
transition from the period-3 ordered state to the paramagnetic phase remains in
the xy universality class. This conclusion is in contrast with a previous
suggestion of mean-field tricritical behavior.Comment: 13 pages (RevTex 3.0), 10 figures available upon request, CRPS-93-0
Magnetic-Field Induced First-Order Transition in the Frustrated XY Model on a Stacked Triangular Lattice
The results of extensive Monte Carlo simulations of magnetic-field induced
transitions in the xy model on a stacked triangular lattice with
antiferromagnetic intraplane and ferromagnetic interplane interactions are
discussed. A low-field transition from the paramagnetic to a 3-state (Potts)
phase is found to be very weakly first order with behavior suggesting
tricriticality at zero field. In addition to clarifying some long-standing
ambiguity concerning the nature of this Potts-like transition, the present work
also serves to further our understanding of the critical behavior at ,
about which there has been much controversy.Comment: 10 pages (RevTex 3.0), 4 figures available upon request, CRPS-93-0
Spectrum of confining strings in SU(N) gauge theories
We study the spectrum of the confining strings in four-dimensional SU(N)
gauge theories. We compute, for the SU(4) and SU(6) gauge theories formulated
on a lattice, the string tensions sigma_k related to sources with Z_N charge k,
using Monte Carlo simulations. Our results are consistent with the sine formula
sigma_k/sigma = sin k pi/N / sin pi/N for the ratio between sigma_k and the
standard string tension sigma.
For the SU(4) and SU(6) cases the accuracy is approximately 1% and 2%,
respectively. The sine formula is known to emerge in various realizations of
supersymmetric SU(N) gauge theories. On the other hand, our results show
deviations from Casimir scaling. We also discuss an analogous behavior
exhibited by two-dimensional SU(N) x SU(N) chiral models.Comment: Latex, 34 pages, 10 figures. Results of new SU(4) simulations added.
The new data are included in the analysis, leading to improved final
estimates for SU(4). Conclusions unchange