arXiv subjects

Ettore Vicari

Publications and source records attributed to Ettore Vicari.

At least 145 records · Page 8Linked to original sources

arXiv2011

Ferromagnetic-glassy transitions in three-dimensional Ising spin glasses

We investigate the ferromagnetic-glassy transitions which separate the low-temperature ferromagnetic and spin-glass phases in the temperature-disorder phase diagram of three-dimensional Ising spin-glass models. For this purpose, we consider the cubic-lattice +-J (Edwards-Anderson) Ising model with bond distribution $P(J) = p δ(J - 1) + (1-p) δ(J + 1)$, and present a numerical Monte Carlo study of the critical behavior along the line that marks the onset of ferromagnetism. The finite-size scaling analysis of the Monte Carlo data shows that the ferromagnetic-glassy transition line is slightly reentrant. As a consequence, for an interval of the disorder parameter p, around p=0.77, the system presents a low-temperature glassy phase, an intermediate ferromagnetic phase, and a high-temperature paramagnetic phase. Along the ferromagnetic-glassy transition line magnetic correlations show a universal critical behavior with critical exponents nu=0.96(2) and eta=-0.39(2). The hyperscaling relation beta/nu = (1 + eta)/2 is satisfied at the transitions, so that beta/nu = 0.305(10). This magnetic critical behavior represents a new universality class for ferromagnetic transitions in Ising-like disordered systems. Overlap correlations are apparently not critical and show a smooth behavior across the transition.

cond-mat.dis-nn↗

arXiv2011

Critical dynamics in trapped particle systems

We discuss the effects of a trapping space-dependent potential on the critical dynamics of lattice gas models. Scaling arguments provide a dynamic trap-size scaling framework to describe how critical dynamics develops in the large trap-size limit. We present numerical results for the relaxational dynamics of a two-dimensional lattice gas (Ising) model in the presence of a harmonic trap, which support the dynamic trap-size scaling scenario.

cond-mat.stat-mech↗

arXiv2011

The entanglement entropy of one-dimensional gases

We introduce a systematic framework to calculate the bipartite entanglement entropy of a spatial subsystem in a one-dimensional quantum gas which can be mapped into a noninteracting fermion system. To show the wide range of applicability of the proposed formalism, we use it for the calculation of the entanglement in the eigenstates of periodic systems, in a gas confined by boundaries or external potentials, in junctions of quantum wires and in a time-dependent parabolic potential.

cond-mat.stat-mech↗

arXiv2011

Scaling of bipartite entanglement in one-dimensional lattice systems with a trapping potential

We study the effects of a power-law trapping potential on the scaling behaviour of the entanglement at the quantum critical point of one-dimensional (1D) lattice particle systems. We compute bipartite von Neumann and Renyi entropies in the presence of the trap, and analyze their scaling behaviour with increasing the trap size. As a theoretical laboratory, we consider the quantum XY chain in an external transverse field acting as a trap for the spinless fermions of its quadratic Hamiltonian representation. We then investigate confined particle systems described by the 1D Bose-Hubbard model in the superfluid phase (around the center of the trap). In both cases conformal field theory predicts logarithmically divergent bipartite entanglement entropies for the homogeneous systems without trap. The presence of the trapping potential breaks conformal invariance, affecting the critical behaviour of the homogeneous system. Our results show that the bipartite entanglement entropies diverge logarithmically with increasing the trap size, and present notable scaling behaviours in the trap-size scaling limit.

cond-mat.stat-mech↗

arXiv2011

Equilibrium and off-equilibrium trap-size scaling in 1D ultracold bosonic gases

We study some aspects of equilibrium and off equilibrium quantum dynamics of dilute bosonic gases in the presence of a trapping potential. We consider systems with a fixed number of particles N and study their scaling behavior with increasing the trap size. We focus on one-dimensional (1D) bosonic systems, such as gases described by the Lieb-Liniger model and its Tonks-Girardeau limit of impenetrable bosons, and gases constrained in optical lattices as described by the Bose-Hubbard model. We study their quantum (zero-temperature) behavior at equilibrium and off equilibrium during the unitary time evolution arising from changes of the trapping potential, which may be instantaneous or described by a power-law time dependence, starting from the equilibrium ground state for a initial trap size. Renormalization-group scaling arguments, analytical and numerical calculations show that the trap-size dependence of the equilibrium and off-equilibrium dynamics can be cast in the form of a trap-size scaling in the low-density regime, characterized by universal power laws of the trap size, in dilute gases with repulsive contact interactions and lattice systems described by the Bose-Hubbard model. The scaling functions corresponding to several physically interesting observables are computed. Our results are of experimental relevance for systems of cold atomic gases trapped by tunable confining potentials.

cond-mat.quant-gas↗

arXiv2010

The three-dimensional gauge-glass model

We investigate the temperature-disorder (T-S) phase diagram of a three-dimensional gauge glass model, which is a cubic-lattice nearest-neighbor XY model with quenched random phase shifts A_xy at the bonds, by numerical Monte Carlo simulations. We consider the uncorrelated phase-shift distribution P(A_xy)\sim \exp[(cos A_xy)/S], which has the pure XY model and the uniform distribution of random shifts as extreme cases at S=0 and S->infty respectively, and which gives rise to equal magnetic and overlap correlation functions when T=S. While the high-temperature phase is always paramagnetic, at low temperatures there is a ferromagnetic phase for weak disorder (small S) and a glassy phase at large disorder (large S). These three phases are separated by transition lines with different magnetic and glassy critical behaviors. The disorder induced by the random shifts turns out to be irrelevant at the paramagnetic-ferromagnetic transition line, where the critical behavior belongs to the 3D XY universality class of pure systems; disorder gives only rise to very slowly decaying scaling corrections. The glassy critical behavior along the finite-temperature paramagnetic-glassy transition line belongs to the gauge-glass universality class, with a quite large critical exponent nu=3.2(4). These transition lines meet at a multicritical point M, located at T=S=0.7840(2). The low-temperature ferromagnetic and glassy phases are separated by a third transition line, from M down to the T=0 axis, which is slightly reentrant.

cond-mat.dis-nn↗

arXiv2010

Quasi-long-range order in trapped systems

We investigate the effects of a trapping space-dependent potential on the low-temperature quasi-long-range order phase of two-dimensional particle systems with a relevant U(1) symmetry, such as quantum atomic gases. We characterize the universal features of the trap-size dependence using scaling arguments. The resulting scenario is supported by numerical Monte Carlo simulations of a classical two-dimensional XY model with a space-dependent hopping parameter whose inhomogeneity is analogous to that arising from the trapping potential in experiments of atomic gases.

cond-mat.stat-mech↗

arXiv2010

Universality of the glassy transitions in the two-dimensional +- J Ising model

We investigate the zero-temperature glassy transitions in the square-lattice +- J Ising model, with bond distribution $P(J_{xy}) = p δ(J_{xy} - J) + (1-p) δ(J_{xy} + J)$; p=1 and p=1/2 correspond to the pure Ising model and to the Ising spin glass with symmetric bimodal distribution, respectively. We present finite-temperature Monte Carlo simulations at p=4/5, which is close to the low-temperature paramagnetic-ferromagnetic transition line located at p=0.89, and at p=1/2. Their comparison provides a strong evidence that the glassy critical behavior that occurs for $1-p_0<p<p_0$, $p_0=0.897$, is universal, i.e., independent of p. Moreover, we show that glassy and magnetic modes are not coupled at the multicritical zero-temperature point where the paramagnetic-ferromagnetic transition line and the T=0 glassy transition line meet. On the theoretical side we discuss the validity of finite-size scaling in glassy systems with a zero-temperature transition and a discrete Hamiltonian spectrum. Because of a freezing phenomenon which occurs in a finite volume at sufficiently low temperatures, the standard finite-size scaling limit in terms of $TL^{1/ν}$ does not exist: the renormalization-group invariant quantity $ξ/L$ should be used instead as basic variable.

cond-mat.dis-nn↗

arXiv2010

Quantum critical behavior and trap-size scaling of trapped bosons in a one-dimensional optical lattice

We study the quantum (zero-temperature) critical behaviors of confined particle systems described by the one-dimensional (1D) Bose-Hubbard model in the presence of a confining potential, at the Mott insulator to superfluid transitions, and within the gapless superfluid phase. Specifically, we consider the hard-core limit of the model, which allows us to study the effects of the confining potential by exact and very accurate numerical results. We analyze the quantum critical behaviors in the large trap-size limit within the framework of the trap-size scaling (TSS) theory, which introduces a new trap exponent theta to describe the dependence on the trap size. This study is relevant for experiments of confined quasi 1D cold atom systems in optical lattices. At the low-density Mott transition TSS can be shown analytically within the spinless fermion representation of the hard-core limit. The trap-size dependence turns out to be more subtle in the other critical regions, when the corresponding homogeneous system has a nonzero filling f, showing an infinite number of level crossings of the lowest states when increasing the trap size. At the n=1 Mott transition this gives rise to a modulated TSS: the TSS is still controlled by the trap-size exponent theta, but it gets modulated by periodic functions of the trap size. Modulations of the asymptotic power-law behavior is also found in the gapless superfluid region, with additional multiscaling behaviors.

cond-mat.stat-mech↗

arXiv2010

Trap-size scaling in confined particle systems at quantum transitions

We develop a trap-size scaling theory for trapped particle systems at quantum transitions. As a theoretical laboratory, we consider a quantum XY chain in an external transverse field acting as a trap for the spinless fermions of its quadratic Hamiltonian representation. We discuss trap-size scaling at the Mott insulator to superfluid transition in the Bose-Hubbard model. We present exact and accurate numerical results for the XY chain and for the low-density Mott transition in the hard-core limit of the one-dimensional Bose-Hubbard model. Our results are relevant for systems of cold atomic gases in optical lattices.

cond-mat.stat-mech↗

arXiv2010

Magnetic and glassy transitions in the square-lattice XY model with random phase shifts

We investigate the magnetic and glassy transitions of the square-lattice XY model in the presence of random phase shifts. We consider two different random-shift distributions: the Gaussian distribution and a slightly different distribution (cosine distribution) which allows the exact determination of the Nishimori line where magnetic and overlap correlation functions are equal. We perform Monte Carlo simulations for several values of the temperature and of the variance of the disorder distribution, in the paramagnetic phase close to the magnetic and glassy transition lines. We find that, along the transition line separating the paramagnetic and the quasi-long-range order phases, magnetic correlation functions show a universal Kosterlitz-Thouless behavior as in the pure XY model, while overlap correlations show a disorder-dependent critical behavior. This behavior is observed up to a multicritical point which, in the cosine model, lies on the Nishimori line. Finally, for large values of the disorder variance, we observe a universal zero-temperature glassy critical transition, which is in the same universality class as that occurring in the gauge-glass model.

cond-mat.stat-mech↗

arXiv2009

Critical behavior and scaling in trapped systems

We study the scaling properties of critical particle systems confined by a potential. Using renormalization-group arguments, we show that their critical behavior can be cast in the form of a trap-size scaling, resembling finite-size scaling theory, with a nontrivial trap critical exponent theta, which describes how the correlation length scales with the trap size l, i.e., $ξ\sim l^θ$ at the critical point. theta depends on the universality class of the transition, the power law of the confining potential, and on the way it is coupled to the critical modes. We present numerical results for two-dimensional lattice gas (Ising) models with various types of harmonic traps, which support the trap-size scaling scenario.

cond-mat.stat-mech↗

arXiv2009

Quasi-long-range order in the 2D XY model with random phase shifts

We study the square-lattice XY model in the presence of random phase shifts. We consider two different disorder distributions with zero average shift and investigate the low-temperature quasi-long-range order phase which occurs for sufficiently low disorder. By means of Monte Carlo simulations we determine several universal quantities which are then compared with the analytic predictions of the random spin-wave theory. We observe a very good agreement which indicates that the universal long-distance behavior in the whole low-disorder low-temperature phase is fully described by the random spin-wave theory.

cond-mat.dis-nn↗

arXiv2008

Critical and multicritical behavior of the +- J Ising model in two and three dimensions

We report our Monte Carlo results on the critical and multicritical behavior of the +- J Ising model [with a random-exchange probability P(J_{xy}) = p δ(J_{xy} - J) + (1-p) δ(J_{xy} + J)], in two and three dimensions. We study the transition line between the paramagnetic and ferromagnetic phase, which extends from p=1 to a multicritical (Nishimori) point. By a finite-size scaling analysis, we provide strong numerical evidence that in three dimensions the critical behavior along this line belongs to the same universality class as that of the critical transition in the randomly dilute Ising model. In two dimensions we confirm that the critical behavior is controlled by the pure Ising fixed point and that disorder is marginally irrelevant, giving rise to universal logarithmic corrections. In both two and three dimensions, we also determine the location of the multicritical Nishimori point, as well as the renormalization-group dimensions of the operators that control the renormalization-group flow close to it.

cond-mat.dis-nn↗

arXiv2008

Large N transition in the 2D SU(N)xSU(N) nonlinear sigma model

We consider the characteristic polynomial associated with the smoothed two point function in two dimensional large N principal chiral model. We numerically show that it undergoes a transition at a critical distance of the order of the correlation length. The transition is in the same universality class as two dimensional large N QCD.

hep-lat↗

arXiv2008

The critical behavior of three-dimensional Ising spin glass models

We perform high-statistics Monte Carlo simulations of three-dimensional Ising spin-glass models on cubic lattices of size L: the +- J (Edwards-Anderson) Ising model for two values of the disorder parameter p, p=0.5 and p=0.7 (up to L=28 and L=20, respectively), and the bond-diluted bimodal model for bond-occupation probability p_b = 0.45 (up to L=16). The finite-size behavior of the quartic cumulants at the critical point allows us to check very accurately that these models belong to the same universality class. Moreover, it allows us to estimate the scaling-correction exponent ωrelated to the leading irrelevant operator: ω=1.0(1). Shorter Monte Carlo simulations of the bond-diluted bimodal models at p_b=0.7 and p_b=0.35 (up to L=10) and of the Ising spin-glass model with Gaussian bond distribution (up to L=8) also support the existence of a unique Ising spin-glass universality class. A careful finite-size analysis of the Monte Carlo data which takes into account the analytic and the nonanalytic corrections to scaling allows us to obtain precise and reliable estimates of the critical exponents νand η: we obtain ν=2.45(15) and η=-0.375(10).

cond-mat.dis-nn↗

arXiv2008

Multicritical Nishimori point in the phase diagram of the +- J Ising model on a square lattice

We investigate the critical behavior of the random-bond +- J Ising model on a square lattice at the multicritical Nishimori point in the T-p phase diagram, where T is the temperature and p is the disorder parameter (p=1 corresponds to the pure Ising model). We perform a finite-size scaling analysis of high-statistics Monte Carlo simulations along the Nishimori line defined by $2p-1={\rm Tanh}(1/T)$, along which the multicritical point lies. The multicritical Nishimori point is located at p^*=0.89081(7), T^*=0.9528(4), and the renormalization-group dimensions of the operators that control the multicritical behavior are y_1=0.655(15) and y_2 = 0.250(2); they correspond to the thermal exponent ν= 1/y_2=4.00(3) and to the crossover exponent ϕ= y_1/y_2=2.62(6).

cond-mat.dis-nn↗

arXiv2008

Static and dynamic structure factors in three-dimensional randomly diluted Ising models

We consider the three-dimensional randomly diluted Ising model and study the critical behavior of the static and dynamic spin-spin correlation functions (static and dynamic structure factors) at the paramagnetic-ferromagnetic transition in the high-temperature phase. We consider a purely relaxational dynamics without conservation laws, the so-called model A. We present Monte Carlo simulations and perturbative field-theoretical calculations. While the critical behavior of the static structure factor is quite similar to that occurring in pure Ising systems, the dynamic structure factor shows a substantially different critical behavior. In particular, the dynamic correlation function shows a large-time decay rate which is momentum independent. This effect is not related to the presence of the Griffiths tail, which is expected to be irrelevant in the critical limit, but rather to the breaking of translational invariance, which occurs for any sample and which, at the critical point, is not recovered even after the disorder average.

cond-mat.dis-nn↗