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P. Butera

Publications and source records attributed to P. Butera.

32 records · Page 2Linked to original sources
arXiv2000

Extension to order $β^{23}$ of the high-temperature expansions for the spin-1/2 Ising model on the simple-cubic and the body-centered-cubic lattices

Using a renormalized linked-cluster-expansion method, we have extended to order $β^{23}$ the high-temperature series for the susceptibility $χ$ and the second-moment correlation length $ξ$ of the spin-1/2 Ising models on the sc and the bcc lattices. A study of these expansions yields updated direct estimates of universal parameters, such as exponents and amplitude ratios, which characterize the critical behavior of $χ$ and $ξ$. Our best estimates for the inverse critical temperatures are $β^{sc}_c=0.221654(1)$ and $β^{bcc}_c=0.1573725(6)$. For the susceptibility exponent we get $γ=1.2375(6)$ and for the correlation length exponent we get $ν=0.6302(4)$. The ratio of the critical amplitudes of $χ$ above and below the critical temperature is estimated to be $C_+/C_-=4.762(8)$. The analogous ratio for $ξ$ is estimated to be $f_+/f_-=1.963(8)$. For the correction-to-scaling amplitude ratio we obtain $a^+_ξ/a^+_χ=0.87(6)$.

hep-lat↗
arXiv1999

Critical specific heats of the N-vector spin models on the sc and the bcc lattices

We have computed through order $β^{21}$ the high-temperature expansions for the nearest-neighbor spin correlation function $G(N,β)$ of the classical N-vector model, with general N, on the simple-cubic and on the body-centered-cubic lattices. For this model, also known in quantum field theory as the lattice O(N) nonlinear sigma model, we have presented in previous papers extended expansions of the susceptibility, of its second field derivative and of the second moment of the correlation function. Here we study the internal specific energy and the specific heat $C(N,β)$, obtaining new estimates of the critical parameters and therefore a more accurate direct test of the hyperscaling relation $d ν(N)=2 - α(N)$ on a range of values of the spin dimensionality N, including N=0 [the self-avoiding walk model], N=1 [the Ising spin 1/2 model], N=2 [the XY model], N=3 [the classical Heisenberg model]. By the newly extended series, we also compute the universal combination of critical amplitudes usually denoted by $R^+_ξ(N)$, in fair agreement with renormalization group estimates.

hep-lat↗
arXiv1999

High temperature study of the Kosterlitz-Thouless phase transition in the XY model on the triangular lattice

High temperature series expansions of the spin-spin correlation function for the XY (or plane rotator) model on the triangular lattice are extended by two terms up to order beta^{14}. Tables of the expansion coefficients are reported for the correlation function spherical moments of order l=0 and 2. Our analysis of the series supports the Kosterlitz-Thouless predictions on the structure of the critical singularities and leads to fairly accurate estimates of the critical parameters.

cond-mat.stat-mech↗
arXiv1998

Monte Carlo simulations and field transformation: the scalar case

We describe a new method in lattice field theory to compute observables at various values of the parameters lambda_i in the action S[phi,lambda_i]. Firstly one performs a single simulation of a ``reference action'' S[phi^r, lambda_i^r] with fixed lambda_i^r. Then the phi^r-configurations are transformed into those of a field phi distributed according to S[phi,lambda_i], apart from a ``remainder action'' which enters as a \break weight. In this way we measure the observables at values of lambda_i different from lambda_i^r. We study the performance of the algorithm in the case of the simplest renormalizable model, namely the phi^4 scalar theory on a four dimensional lattice and compare the method with the ``histogram'' technique of which it is a generalization.

hep-lat↗
arXiv1998

Renormalized couplings and scaling correction amplitudes in the N-vector spin models on the sc and the bcc lattices

For the classical N-vector model, with arbitrary N, we have computed through order β^{17} the high temperature expansions of the second field derivative of the susceptibility χ_4(N,β) on the simple cubic and on the body centered cubic lattices. (The N-vector model is also known as the O(N) symmetric classical spin Heisenberg model or, in quantum field theory, as the lattice O(N) nonlinear sigma model.) By analyzing the expansion of χ_4(N,β) on the two lattices, and by carefully allowing for the corrections to scaling, we obtain updated estimates of the critical parameters and more accurate tests of the hyperscaling relation dν(N) +γ(N) -2Δ_4(N)=0 for a range of values of the spin dimensionality N, including N=0 [the self-avoiding walk model], N=1 [the Ising spin 1/2 model], N=2 [the XY model], N=3 [the classical Heisenberg model]. Using the recently extended series for the susceptibility and for the second correlation moment, we also compute the dimensionless renormalized four point coupling constants and some universal ratios of scaling correction amplitudes in fair agreement with recent renormalization group estimates.

hep-lat↗
arXiv1997

Perturbative renormalization group, exact results and high temperature series to order 21 for the N-vector spin models on the square lattice

High temperature expansions for the susceptibility and the second correlation moment of the classical N-vector model (also known as the O(N) symmetric Heisenberg classical spin model or the as the lattice O(N) nonlinear sigma model) on the square lattice are extended from order beta^{14} to beta^{21} for arbitrary N. For the second field derivative of the susceptibility the series expansion is extended from order beta^{14} to beta^{17}. For -2 < N < 2, a numerical analysis of the series is performed in order to compare the critical exponents gamma(N), nu(N) and Delta(N) to exact (though nonrigorous) formulas and to compute the "dimensionless four point coupling constant" g_r(N). For N > 2, we present a study of the analiticity properties of chi, xi etc. in the complex beta-plane and describe a method to estimate the parameters which characterize their low-temperature behaviors. We compare our series estimates to the predictions of the perturbative renormalization group theory, to exact (but nonrigorous or conjectured) formulas and to the results of the 1/N expansion, always finding a good agreement.

hep-lat↗
arXiv1997

Critical parameters of N-vector spin models on 3d lattices from high temperature series extended to order beta^{21}

High temperature expansions for the free energy, the susceptibility and the second correlation moment of the classical N-vector model [also denoted as the O(N) symmetric classical spin Heisenberg model or as the lattice O(N) nonlinear sigma model] have been extended to order beta^{21} on the simple cubic and the body centered cubic lattices, for arbitrary N. The series for the second field derivative of the susceptibility has been extended to order beta^{17}. An analysis of the newly computed series yields updated estimates of the model's critical parameters in good agreement with present renormalization group estimates.

hep-lat↗
arXiv1997

N-vector spin models on the sc and the bcc lattices: a study of the critical behavior of the susceptibility and of the correlation length by high temperature series extended to order beta^{21}

High temperature expansions for the free energy, the susceptibility and the second correlation moment of the classical N-vector model [also known as the O(N) symmetric classical spin Heisenberg model or as the lattice O(N) nonlinear sigma model] on the sc and the bcc lattices are extended to order beta^{21} for arbitrary N. The series for the second field derivative of the susceptibility is extended to order beta^{17}. An analysis of the newly computed series for the susceptibility and the (second moment) correlation length yields updated estimates of the critical parameters for various values of the spin dimensionality N, including N=0 [the self-avoiding walk model], N=1 [the Ising spin 1/2 model], N=2 [the XY model], N=3 [the Heisenberg model]. For all values of N, we confirm a good agreement with the present renormalization group estimates. A study of the series for the other observables will appear in a forthcoming paper.

hep-lat↗
arXiv1997

The 2n-point renormalized coupling constants in the 3d Ising model: estimates by high temperature series to order beta^17

We compute the 2n-point renormalized coupling constants in the symmetric phase of the 3d Ising model on the sc lattice in terms of the high temperature expansions O(beta^{17}) of the Fourier transformed 2n-point connected correlation functions at zero momentum. Our high temperature estimates of these quantities, which enter into the small field expansion of the effective potential for a 3d scalar field at the IR fixed point or, equivalently, in the critical equation of state of the 3d Ising model universality class, are compared with recent results obtained by renormalization group methods, strong coupling, stochastic simulations as well as previous high temperature expansions.

hep-lat↗
arXiv1993

Critical exponents of the three-dimensional classical plane rotator model on the sc lattice from a high temperature series analysis

High temperature series expansions of the spin-spin correlation function for the plane rotator (or XY) model on the sc lattice are extended by three terms through order $β^{17}$. Tables of the expansion coefficients are reported for the correlation function spherical moments of order $l=0,1,2$. Our analysis of the series leads to fairly accurate estimates of the critical parameters.

hep-lat↗
arXiv1992

A quantitative study of the Kosterlitz-Thouless phase transition in a system of two-dimensional plane rotators ( XY model ) by high temperature expansions through $β^{20}$

High temperature series expansions of the spin-spin correlation function for the plane rotator (or XY) model on the square lattice are extended by three terms through order $β^{20}$. Tables of the expansion coefficients are reported for the correlation function spherical moments of order $l=0,1,2$. The expansion coefficients through $β^{15}$ for the vorticity are also tabulated. Our analysis of the series supports the Kosterlitz-Thouless predictions on the structure of the critical singularities and leads to fairly accurate estimates of the critical parameters.

hep-lat↗
arXiv1992

High-Temperature series for the $RP^{n-1}$ lattice spin model (generalized Maier-Saupe model of nematic liquid crystals) in two space dimensions and with general spin dimensionality n

High temperature series expansions of the spin-spin correlation functions of the RP^{n-1} spin model on the square lattice are computed through order beta^{8} for general spin dimensionality n. Tables are reported for the expansion coefficients of the energy per site, the susceptibility and the second correlation moment.

hep-lat↗