Author
Ettore Vicari
Other affiliations: Boston University, Istituto Nazionale di Fisica Nucleare, Dalhousie University
Bio: Ettore Vicari is an academic researcher from University of Pisa. The author has contributed to research in topics: Ising model & Critical exponent. The author has an hindex of 46, co-authored 360 publications receiving 9263 citations. Previous affiliations of Ettore Vicari include Boston University & Istituto Nazionale di Fisica Nucleare.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this paper, the critical behavior of spin systems at equilibrium is studied in three and two dimensions, and the results in three-dimensional space are presented in particular for the six-loop perturbative series for the β -functions.
1,363 citations
TL;DR: In this article, the critical exponents for the three-dimensional Heisenberg universality class were improved by combining Monte Carlo simulations based on finite-size scaling methods and high-temperature expansions.
Abstract: We improve the theoretical estimates of the critical exponents for the three-dimensional Heisenberg universality class. We find $\ensuremath{\gamma}=1.3960(9),$ $\ensuremath{
u}=0.7112(5),$ $\ensuremath{\eta}=0.0375(5),$ $\ensuremath{\alpha}=\ensuremath{-}0.1336(15),$ $\ensuremath{\beta}=0.3689(3),$ and $\ensuremath{\delta}=4.783(3).$ We consider an improved lattice ${\ensuremath{\varphi}}^{4}$ Hamiltonian with suppressed leading scaling corrections. Our results are obtained by combining Monte Carlo simulations based on finite-size scaling methods and high-temperature expansions. The critical exponents are computed from high-temperature expansions specialized to the ${\ensuremath{\varphi}}^{4}$ improved model. By the same technique we determine the coefficients of the small-magnetization expansion of the equation of state. This expansion is extended analytically by means of approximate parametric representations, obtaining the equation of state in the whole critical region. We also determine a number of universal amplitude ratios.
345 citations
TL;DR: In this article, the authors improved the theoretical estimates of the critical exponents for the three-dimensional universality class by combining Monte Carlo simulations based on finite-size scaling methods, and high-temperature expansions.
Abstract: We improve the theoretical estimates of the critical exponents for the three-dimensional $\mathrm{XY}$ universality class. We find $\ensuremath{\alpha}=\ensuremath{-}0.0146(8),$ $\ensuremath{\gamma}=1.3177(5),$ $\ensuremath{
u}=0.67155(27),$ $\ensuremath{\eta}=0.0380(4),$ $\ensuremath{\beta}=0.3485(2),$ and $\ensuremath{\delta}=4.780(2).$ We observe a discrepancy with the most recent experimental estimate of $\ensuremath{\alpha};$ this discrepancy calls for further theoretical and experimental investigations. Our results are obtained by combining Monte Carlo simulations based on finite-size scaling methods, and high-temperature expansions. Two improved models (with suppressed leading scaling corrections) are selected by Monte Carlo computation. The critical exponents are computed from high-temperature expansions specialized to these improved models. By the same technique we determine the coefficients of the small-magnetization expansion of the equation of state. This expansion is extended analytically by means of approximate parametric representations, obtaining the equation of state in the whole critical region. We also determine the specific-heat amplitude ratio.
300 citations
TL;DR: In this article, the authors improved the theoretical estimates of the critical exponents for the three-dimensional universality class that apply to the superfluid transition in $^{4}\mathrm{He} along the $\ensuremath{\lambda}$ line of its phase diagram.
Abstract: We improve the theoretical estimates of the critical exponents for the three-dimensional $XY$ universality class that apply to the superfluid transition in $^{4}\mathrm{He}$ along the $\ensuremath{\lambda}$ line of its phase diagram. We obtain the estimates $\ensuremath{\alpha}=\ensuremath{-}0.0151(3)$, $\ensuremath{
u}=0.6717(1)$, $\ensuremath{\eta}=0.0381(2)$, $\ensuremath{\gamma}=1.3178(2)$, $\ensuremath{\beta}=0.3486(1)$, and $\ensuremath{\delta}=4.780(1)$. Our results are obtained by finite-size scaling analyses of high-statistics Monte Carlo simulations up to lattice size $L=128$ and resummations of 22nd-order high-temperature expansions of two improved models with suppressed leading scaling corrections. We note that our result for the specific-heat exponent $\ensuremath{\alpha}$ disagrees with the most recent experimental estimate $\ensuremath{\alpha}=\ensuremath{-}0.0127(3)$ at the superfluid transition of $^{4}\mathrm{He}$ in a microgravity environment.
210 citations
TL;DR: 25th-order high-temperature series are computed for a general nearest-neighbor three-dimensional Ising model with arbitrary potential on the simple cubic lattice and three improved potentials characterized by suppressed leading scaling corrections are considered.
Abstract: 25th-order high-temperature series are computed for a general nearest-neighbor three-dimensional Ising model with arbitrary potential on the simple cubic lattice. In particular, we consider three improved potentials characterized by suppressed leading scaling corrections. Critical exponents are extracted from high-temperature series specialized to improved potentials, obtaining $\ensuremath{\gamma}=1.2373(2),$ $\ensuremath{
u}=0.63012(16),$ $\ensuremath{\alpha}=0.1096(5),$ $\ensuremath{\eta}=0.03639(15),$ $\ensuremath{\beta}=0.32653(10),$ and $\ensuremath{\delta}=4.7893(8).$ Moreover, biased analyses of the 25th-order series of the standard Ising model provide the estimate $\ensuremath{\Delta}=0.52(3)$ for the exponent associated with the leading scaling corrections. By the same technique, we study the small-magnetization expansion of the Helmholtz free energy. The results are then applied to the construction of parametric representations of the critical equation of state, using a systematic approach based on a global stationarity condition. Accurate estimates of several universal amplitude ratios are also presented.
196 citations
Cited by
More filters
TL;DR: Wentzel and Jauch as discussed by the authors described the symmetrization of the energy momentum tensor according to the Belinfante Quantum Theory of Fields (BQF).
Abstract: To say that this is the best book on the quantum theory of fields is no praise, since to my knowledge it is the only book on this subject But it is a very good and most useful book The original was written in German and appeared in 1942 This is a translation with some minor changes A few remarks have been added, concerning meson theory and nuclear forces, also footnotes referring to modern work in this field, and finally an appendix on the symmetrization of the energy momentum tensor according to Belinfante Quantum Theory of Fields Prof Gregor Wentzel Translated from the German by Charlotte Houtermans and J M Jauch Pp ix + 224, (New York and London: Interscience Publishers, Inc, 1949) 36s
2,935 citations
TL;DR: Proxy curves relating observed signal-to-noise ratios to average measurement uncertainties show promise to provide useful expected measurement error estimates in the absence of the long time-series needed for temporal subsetting.
Abstract: SUMMARY Ambient noise tomography is a rapidly emerging field of seismological research. This paper presents the current status of ambient noise data processing as it has developed over the past several years and is intended to explain and justify this development through salient examples. The ambient noise data processing procedure divides into four principal phases: (1) single station data preparation, (2) cross-correlation and temporal stacking, (3) measurement of dispersion curves (performed with frequency‐time analysis for both group and phase speeds) and (4) quality control, including error analysis and selection of the acceptable measurements. The procedures that are described herein have been designed not only to deliver reliable measurements, but to be flexible, applicable to a wide variety of observational settings, as well as being fully automated. For an automated data processing procedure, data quality control measures are particularly important to identify and reject bad measurements and compute quality assurance statistics for the accepted measurements. The principal metric on which to base a judgment of quality is stability, the robustness of the measurement to perturbations in the conditions under which it is obtained. Temporal repeatability, in particular, is a significant indicator of reliability and is elevated to a high position in our assessment, as we equate seasonal repeatability with measurement uncertainty. Proxy curves relating observed signal-to-noise ratios to average measurement uncertainties show promise to provide useful expected measurement error estimates in the absence of the long time-series needed for temporal subsetting.
1,798 citations
TL;DR: Baxter has inherited the mantle of Onsager who started the process by solving exactly the two-dimensional Ising model in 1944 as mentioned in this paper, and there has been a growing belief that all the twodimensional lattice statistical models will eventually be solved and that it will be Professor Baxter who solves them.
Abstract: R J Baxter 1982 London: Academic xii + 486 pp price £43.60 Over the past few years there has been a growing belief that all the twodimensional lattice statistical models will eventually be solved and that it will be Professor Baxter who solves them. Baxter has inherited the mantle of Onsager who started the process by solving exactly the two-dimensional Ising model in 1944.
1,658 citations
TL;DR: In this article, the authors review recent developments in the physics of ultracold atomic and molecular gases in optical lattices and show how these systems may be employed as quantum simulators to answer some challenging open questions of condensed matter, and even high energy physics.
Abstract: We review recent developments in the physics of ultracold atomic and molecular gases in optical lattices. Such systems are nearly perfect realisations of various kinds of Hubbard models, and as such may very well serve to mimic condensed matter phenomena. We show how these systems may be employed as quantum simulators to answer some challenging open questions of condensed matter, and even high energy physics. After a short presentation of the models and the methods of treatment of such systems, we discuss in detail, which challenges of condensed matter physics can be addressed with (i) disordered ultracold lattice gases, (ii) frustrated ultracold gases, (iii) spinor lattice gases, (iv) lattice gases in “artificial” magnetic fields, and, last but not least, (v) quantum information processing in lattice gases. For completeness, also some recent progress related to the above topics with trapped cold gases will be discussed. Motto: There are more things in heaven and earth, Horatio, Than are dreamt of in your...
1,535 citations
TL;DR: In this paper, the critical behavior of spin systems at equilibrium is studied in three and two dimensions, and the results in three-dimensional space are presented in particular for the six-loop perturbative series for the β -functions.
1,363 citations