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M. Comi

Publications and source records attributed to M. Comi.

At least 19 recordsLinked to original sources
arXiv2005

The ϕ_3^4 lattice field theory viewed from the high-temperature side

We analyze high-temperature series expansions of the two-point and four-point correlation-functions in the three-dimensional euclidean lattice scalar field theory with quartic self-coupling, which have been recently extended through twenty-fifth order for the simple-cubic and body-centered-cubic lattices. We conclude that the length of the present series is sufficient for a fairly accurate description of the critical behavior of the model and confirm the validity of universality, scaling and hyperscaling. In the case of the body-centered-cubic lattice, we determine the value of the quartic self-coupling for which the leading corrections to scaling approximately vanish and correspondingly the universal critical parameters can be determined with high accuracy. In particular, for the susceptibility and the correlation-length exponents we find γ=1.2373(2) and ν=0.6301(2). For the four-point renormalized coupling we find g=23.56(3). In the case of the simple-cubic lattice our results are consistent with earlier estimates.

hep-lat↗
arXiv2004

Updated tests of scaling and universality for the spin-spin correlations in the 2D and 3D spin-S Ising models using high-temperature expansions

We have extended, from order 12 through order 25, the high-temperature series expansions (in zero magnetic field) for the spin-spin correlations of the spin-S Ising models on the square, simple-cubic and body-centered-cubic lattices. On the basis of this large set of data, we confirm accurately the validity of the scaling and universality hypotheses by resuming several tests which involve the correlation function, its moments and the exponential or the second-moment correlation-lengths.

hep-lat↗
arXiv2003

Critical parameters and universal amplitude ratios of two-dimensional spin-S Ising models using high- and low-temperature expansions

For the study of Ising models of general spin S on the square lattice, we have combined our recently extended high-temperature expansions with the low-temperature expansions derived some time ago by Enting, Guttmann and Jensen. We have computed for the first time various critical parameters and improved the estimates of others. Moreover the properties of hyperscaling and of universality (spin S independence) of exponents and of various dimensionless amplitude combinations have been verified accurately. Assuming the validity of the lattice-lattice scaling, from our estimates of critical amplitudes for the square lattice we have also obtained estimates of the corresponding amplitudes for the spin S Ising model on the triangular, honeycomb, and kagome` lattices.

hep-lat↗
arXiv2002

A library of extended high-temperature expansions of basic observables for the spin S Ising models on two- and three-dimensional lattices

We present an on-line library of unprecedented extension for high-temperature expansions of basic observables in the Ising models of general spin S, with nearest-neighbor interactions. We have tabulated through order beta^{25} the series for the nearest-neighbor correlation function, the susceptibility and the second correlation moment in two dimensions on the square lattice, and, in three dimensions, on the simple-cubic and the body-centered cubic lattices. The expansion of the second field derivative of the susceptibility is also tabulated through beta^{23} for the same lattices. We have thus added several terms (from four up to thirteen) to the series already published for spin S=1/2,1,3/2,2,5/2,3,7/2,4,5,infinity.

hep-lat↗
arXiv2001

Critical universality and hyperscaling revisited for Ising models of general spin using extended high-temperature series

We have extended through beta^{23} the high-temperature expansion of the second field derivative of the susceptibility for Ising models of general spin, with nearest-neighbor interactions, on the simple cubic and the body-centered cubic lattices. Moreover the expansions for the nearest-neighbor correlation function, the susceptibility and the second correlation moment have been extended up to beta^{25}. Taking advantage of these new data, we can improve the accuracy of direct estimates of critical exponents and of hyper-universal combinations of critical amplitudes such as the renormalized four-point coupling g_r or the quantity usually denoted by R^{+}_{xi}. We have used a variety of series extrapolation procedures and, in some of the analyses, we have assumed that the leading correction-to-scaling exponent theta is universal and roughly known. We have also verified, to high precision, the validity of the hyperscaling relation and of the universality property both with regard to the lattice structure and to the value of the spin.

hep-lat↗
arXiv2001

A remark on the numerical validation of triviality for scalar field theories using high-temperature expansions

We suggest a simple modification of the usual procedures of analysis for the high-temperature (strong-coupling or hopping-parameter) expansions of the renormalized four-point coupling constant in the fourdimensional phi^4 lattice scalar field theory. As a result we can more convincingly validate numerically the triviality of the continuum limit taken from the high temperature phase.

hep-th↗
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

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↗