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Paolo Butera

Publications and source records attributed to Paolo Butera.

11 recordsLinked to original sources
arXiv2013

Higher order expansions for the entropy of a dimer or a monomer-dimer system on d-dimensional lattices

Recently an expansion as a power series in 1/d has been presented for the specific entropy of a complete dimer covering of a d-dimensional hypercubic lattice. This paper extends from 3 to 10 the number of terms known in the series. Likewise an expansion for the entropy, dependent on the dimer-density p, of a monomer-dimer system, involving a sum sum_k a_k(d) p^k, has been recently offered. We herein extend the number of the known expansion coefficients from 6 to 20 for the hyper-cubic lattices of general dimension d and from 6 to 24 for the hyper-cubic lattices of dimensions d < 5 . We show that this extension can lead to accurate numerical estimates of the p-dependent entropy for lattices with dimension d > 2. The computations of this paper have led us to make the following marvelous conjecture: "In the case of the hyper-cubic lattices, all the expansion coefficients, a_k(d), are positive"! This paper results from a simple melding of two disparate research programs: one computing to high orders the Mayer series coefficients of a dimer gas, the other studying the development of entropy from these coefficients. An effort is made to make this paper self-contained by including a review of the earlier works.

hep-lat↗
arXiv2013

The two-dimensional 4-state Potts model in a magnetic field

We present a solution of the non-linear renormalization group equations leading to the dominant and subdominant singular behaviours of physical quantities (free energy density, correlation length, internal energy, specific heat, magnetization, susceptibility and magnetocaloric coefficient) at the critical temperature in a non- vanishing magnetic field. The solutions i) lead to exact cancellation of logarithmic corrections in universal amplitude ratios and ii) prove recently proposed relations among logarithmic exponents.

hep-lat↗
arXiv2012

Yang-Lee edge singularities from extended activity expansions of the dimer density for bipartite lattices of dimensionality 2 <= d <= 7

We have extended, in most cases through 24th order, the series expansions of the dimer density in powers of the activity in the case of bipartite ((hyper)-simple-cubic and (hyper)-body-centered-cubic) lattices of dimensionalities 2<= d <= 7. A numerical analysis of these data yields estimates of the exponents characterizing the Yang-Lee edge-singularities for lattice ferromagnetic spin-models as d varies between the lower and the upper critical dimensionalities. Our results are consistent with, but more extensive and sometimes more accurate than those obtained from the existing dimer series or from the estimates of related exponents for lattice animals, branched polymers and fluids. We mention also that it is possible to obtain estimates of the dimer constants from our series for the various lattices.

cond-mat.stat-mech↗
arXiv2011

Triviality problem and the high-temperature expansions of the higher susceptibilities for the Ising and the scalar field models on four-, five- and six-dimensional lattices

High-temperature expansions are presently the only viable approach to the numerical calculation of the higher susceptibilities for the spin and the scalar-field models on high-dimensional lattices. The critical amplitudes of these quantities enter into a sequence of universal amplitude-ratios which determine the critical equation of state. We have obtained a substantial extension through order 24, of the high-temperature expansions of the free energy (in presence of a magnetic field) for the Ising models with spin s >= 1/2 and for the lattice scalar field theory with quartic self-interaction, on the simple-cubic and the body-centered-cubic lattices in four, five and six spatial dimensions. A numerical analysis of the higher susceptibilities obtained from these expansions, yields results consistent with the widely accepted ideas, based on the renormalization group and the constructive approach to Euclidean quantum field theory, concerning the no-interaction ("triviality") property of the continuum (scaling) limit of spin-s Ising and lattice scalar-field models at and above the upper critical dimensionality.

hep-lat↗
arXiv2008

Universal ratios of critical amplitudes in the Potts model universality class

Monte Carlo (MC) simulations and series expansions (SE) data for the energy, specific heat, magnetization, and susceptibility of the three-state and four-state Potts model and Baxter-Wu model on the square lattice are analyzed in the vicinity of the critical point in order to estimate universal combinations of critical amplitudes. We also form effective ratios of the observables close to the critical point and analyze how they approach the universal critical-amplitude ratios. In particular, using the duality relation, we show analytically that for the Potts model with a number of states $q\le 4$, the effective ratio of the energy critical amplitudes always approaches unity linearly with respect to the reduced temperature. This fact leads to the prediction of relations among the amplitudes of correction-to-scaling terms of the specific heat in the low- and high-temperature phases. It is a common belief that the four-state Potts and the Baxter-Wu model belong to the same universality class. At the same time, the critical behavior of the four-state Potts model is modified by logarithmic corrections while that of the Baxter-Wu model is not. Numerical analysis shows that critical amplitude ratios are very close for both models and, therefore, gives support to the hypothesis that the critical behavior of both systems is described by the same renormalization group fixed point.

cond-mat.stat-mech↗
arXiv2008

Numerical revision of the universal amplitude ratios for the two-dimensional 4-state Potts model

Monte Carlo (MC) simulations and series expansion (SE) data for the energy, specific heat, magnetization and susceptibility of the ferromagnetic 4-state Potts model on the square lattice are analyzed in a vicinity of the critical point in order to estimate universal combinations of critical amplitudes. The quality of the fits is improved using predictions of the renormalization group (RG) approach and of conformal invariance, and restricting the data within an appropriate temperature window. The RG predictions on the cancelation of the logarithmic corrections in the universal amplitude ratios are tested. A direct calculation of the effective ratio of the energy amplitudes using duality relations explicitly demonstrates this cancelation of logarithms, thus supporting the predictions of RG. We emphasize the role of corrections of background terms on the determination of the amplitudes. The ratios of the critical amplitudes of the susceptibilities obtained in our analysis differ significantly from those predicted theoretically and supported by earlier SE and MC analysis. This disagreement might signal that the two-kink approximation used in the analytical estimates is not sufficient to describe with fair accuracy the amplitudes of the 4-state model.

cond-mat.stat-mech↗
arXiv2007

A study of logarithmic corrections and universal amplitude ratios in the two-dimensional 4-state Potts model

Monte Carlo (MC) and series expansion (SE) data for the energy, specific heat, magnetization and susceptibility of the two-dimensional 4-state Potts model in the vicinity of the critical point are analysed. The role of logarithmic corrections is discussed and an approach is proposed in order to account numerically for these corrections in the determination of critical amplitudes. Accurate estimates of universal amplitude ratios $A_+/A_-$, $Γ_+/Γ_-$, $Γ_T/Γ_-$ and $R_C^\pm$ are given, which arouse new questions with respect to previous works.

cond-mat.stat-mech↗
arXiv2007

Logarithmic corrections and universal amplitude ratios in the 4-state Potts model

Monte Carlo and series expansion data for the energy, specific heat, magnetisation and susceptibility of the 4-state Potts model in the vicinity of the critical point are analysed. The role of logarithmic corrections is discussed. Estimates of universal ratios A_+/A_-, $Γ_+/Γ_L$, $Γ_T/Γ_L$ and R_c^+ are given.

cond-mat.stat-mech↗
arXiv2001

Susceptibility amplitude ratio in the two-dimensional three-state Potts model

We analyze Monte Carlo simulation and series-expansion data for the susceptibility of the three-state Potts model in the critical region. The amplitudes of the susceptibility on the high- and the low-temperature sides of the critical point as extracted from the Monte Carlo data are in good agreement with those obtained from the series expansions and their (universal) ratio compares quite well with a recent quantum field theory prediction by Delfino and Cardy.

cond-mat.stat-mech↗
arXiv1998

The RANLUX generator: resonances in a random walk test

Using a recently proposed directed random walk test, we systematically investigate the popular random number generator RANLUX developed by Luescher and implemented by James. We confirm the good quality of this generator with the recommended luxury level. At a smaller luxury level (for instance equal to 1) resonances are observed in the random walk test. We also find that the lagged Fibonacci and Subtract-with-Carry recipes exhibit similar failures in the random walk test. A revised analysis of the corresponding dynamical systems leads to the observation of resonances in the eigenvalues of Jacobi matrix.

hep-lat↗