Massimo Campostrini

Critical behavior of the three-dimensional XY universality class

We improve the theoretical estimates of the critical exponents for the three-dimensional XY universality class. We find alpha=-0.0146(8), gamma=1.3177(5), nu=0.67155(27), eta=0.0380(4), beta=0.3485(2), and delta=4.780(2). We observe a discrepancy with the most recent experimental estimate of 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.

Critical exponents and equation of state of the three-dimensional Heisenberg universality class

We improve the theoretical estimates of the critical exponents for the three-dimensional Heisenberg universality class. We find gamma=1.3960(9), nu=0.7112(5), eta=0.0375(5), alpha=-0.1336(15), beta=0.3689(3), and delta=4.783(3). We consider an improved lattice phi^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 phi^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.

25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple cubic lattice

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 gamma=1.2373(2), nu=0.63012(16), alpha=0.1096(5), eta=0.036 39(15), beta=0.326 53(10), and delta=4.78 93(8). Moreover, biased analyses of the 25th-order series of the standard Ising model provide the estimate 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.

The topological susceptibility on the lattice

Abstract We study the multiplicative renormalization of the topological charge operator on the lattice with respect to the continuum. Apparent discrepancies between different methods of determination of the topological charge on the lattice are explained by our result.

Theoretical estimates of the critical exponents of the superfluid transition in {sup 4}He by lattice methods

We improve the theoretical estimates of the critical exponents for the three-dimensional XY universality class that apply to the superfluid transition in {sup 4}He along the {lambda} line of its phase diagram. We obtain the estimates {alpha}=-0.0151(3), {nu}=0.6717(1), {eta}=0.0381(2), {gamma}=1.3178(2), {beta}=0.3486(1), and {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 {alpha} disagrees with the most recent experimental estimate {alpha}=-0.0127(3) at the superfluid transition of {sup 4}He in a microgravity environment.

Topological charge, renormalization and cooling on the lattice☆

Abstract We show that a definition of the topological susceptibility χ on the lattice in terms of local fields, with the proper additive and multiplicative renormalizations, is well defined, self-consistent and compatible with results we obtain by the cooling method. Moreover, we can follow the behaviour of the multiplicative renormalization during cooling, and check its dependence on the coupling constant.

Correlation Length of the Vacuum Condensate in Lattice Gauge Theories

The correlation length λ of the vacuum condensateG2 is determined by Montecarlo simulation of anSU(2) lattice gauge theory. The result isG2 λ4 = 0.0019 ± 0.0002. The implications of this result are discussed.

Parity effects in the scaling of block entanglement in gapless spin chains.

We consider the Rényi alpha entropies for Luttinger liquids (LL). For large block lengths l, these are known to grow like lnl. We show that there are subleading terms that oscillate with frequency 2k{F} (the Fermi wave number of the LL) and exhibit a universal power-law decay with l. The new critical exponent is equal to K/(2alpha), where K is the LL parameter. We present numerical results for the anisotropic XXZ model and the full analytic solution for the free fermion (XX) point.

Cooling and the string tension in lattice gauge theories

Abstract We explore the possibility of improving the determination of the string tension using the cooling method. We present preliminary results for the gauge group SU(2): We find that statistical errors are drastically reduced and at the same time the string tension is preserved through many cooling steps.

High precision study of the structure of D = 4 supersymmetric Yang-Mills quantum mechanics

The spectrum of D = 4 supersymmetric Yang-Mills quantum mechanics is computed with high accuracy in all channels of angular momentum and fermion number. Localized and non-localized states coexists in certain channels as a consequence of the supersymmetric interactions with flat valleys. All states fall into well identifiable supermultiplets providing an explicit realization of supersymmetry on the spectroscopic level. An accidental degeneracy among some supermultiplets has been found. Regularized Witten index converges to a time-independent constant which agrees with earlier calculations.