arXiv subjects

Fabrizio Baroni

Publications and source records attributed to Fabrizio Baroni.

8 recordsLinked to original sources

arXiv2020

Necessary and sufficient conditions for $\mathbb{Z}_2$-symmetry-breaking phase transitions

In a recent paper a toy model (hypercubic model) undergoing a first-order $\mathbb{Z}_2$-symmetry-breaking phase transition ($\mathbb{Z}_2$-SBPT) was introduced. The hypercubic model was inspired by the \emph{topological hypothesis}, according to which a phase transition may be entailed by suitable topological changes of the equipotential surfaces ($Σ_v$'s) of configuration space. In this paper we show that at the origin of a $\mathbb{Z}_2$-SBPT there is a geometric property of the $Σ_v$'s, i.e., dumbbell-shaped $Σ_v$'s suitably defined, which includes a topological change as a limiting case. This property is necessary and sufficient condition to entail a $\mathbb{Z}_2$-SBPT. This new approach has been applied to three models: a modified version introduced here of the hypercubic model, a model introduced in a recent paper with a continuous $\mathbb{Z}_2$-SBPT belonging to several universality classes, and finally to a physical models, i.e., the mean-field $ϕ^4$ model and a simplified version of it.

cond-mat.stat-mech↗

arXiv2020

Models with symmetry-breaking phase transitions triggered by dumbbell-shaped equipotential surfaces

In some recent papers some sufficiency conditions for the occurrence of a $\mathbb{Z}_2$-symmetry breaking phase transition ($\mathbb{Z}_2$-SBPT) have been showed starting from geometric-topological concepts of potential energy landscapes. In particular, a $\mathbb{Z}_2$-SBPT can be triggered by double-well potentials, or in an equivalent way, by dumbbell-shaped equipotential surfaces. In this paper we introduce two models with a $\mathbb{Z}_2$-SBPT which, due to their essential feature, show in the clearest way the generating-mechanism of a $\mathbb{Z}_2$-SBPT above mentioned. These models, despite they cannot be considered physical models, have all the features of such models with the same kind of SBPT. At the end of the paper, the $ϕ^4$ model is revisited in the light of this approach. In particular, the landscape of one of the model introduced here is turned out to be equivalent to that of the mean-field $ϕ^4$ model in a simplified version.

cond-mat.stat-mech↗

arXiv2019

Simplified energy landscape of the $\phi^4$ model and the phase transition

The on lattice $\phi^4$ model is a paradigmatic example of continuous real variables model undergoing a continuous symmetry braking phase transition (SBPT). In this paper we study the $\mathbb{Z}_2$-symmetric mean-field version without the quadratic term of the local potential. Obviously, the simplification is directly extensible to the other symmetry groups for which the model undergoes a SBPT. We show that the $\mathbb{Z}_2$-SBPT is not affected by the quadratic term, and that the potential energy landscape turns out greatly simplified. In particular, there exist only three critical points, to confront with an amount growing as $e^N$ ($N$ is the number of degrees of freedom) of the model with non-vanishing quadratic term. In our opinion, this is an crucial feature because in recent years the study of the link between statistical mechanic and geometric-topological properties of configuration space has received an increasing attention. In this paper we study the equipotential hypersurfaces with the aim of deepening our understanding of the link between SBPTs and the truly essential geometric-topological properties of the energy potential landscape.

cond-mat.stat-mech↗

arXiv2019

Topology of configuration space of the mean-field phi^4 model by Morse theory

In this paper we present the study of the topology of the equipotential hypersurfaces of configuration space of the mean-field $ϕ^4$ model with a $\mathbb{Z}_2$ symmetry. Our purpose is discovering, if any, the relation between the second-order $\mathbb{Z}_2$-symmetry breaking phase transition and the geometric entities mentioned above. The mean-field interaction allows us to solve analytically either the thermodynamic in the canonical ensemble or the topology by means of Morse theory. We have analyzed the results at the light of two theorems on sufficiency conditions for symmetry breaking phase transitions recently proven. This study makes part of a research line based on the general framework of geometric-topological approach to Hamiltonian chaos and critical phenomena.

cond-mat.stat-mech↗

arXiv2017

Phase transitions triggered by dumbbell equipotential hypersurfaces

In a recent paper a toy model (called hypercubic model) undergoing a first-order $\mathbb{Z}_2$ symmetry breaking phase transition (SBPT) has been introduced. The hypercubic model was inspired by the \emph{topological hypothesis}, according to which a phase transition may be entailed by suitable topological changes of the equipotential hypersurfaces $Σ_v$ of configuration space. The $Σ_v$'s of the hypercubic model have a single topological change, which, under further particular hypotheses of geometric nature, entails the $\mathbb{Z}_2$-SBPT. In this paper we introduce an extended version of the hypercubic model in which no topological change in the $Σ_v$'s is present anymore, but nevertheless the $\mathbb{Z}_2$-SBPT occurs the same. We introduce a geometric property of the $Σ_v$'s (i.e. dumbbell $Σ_v$'s suitably defined) that is sufficient to entail a $\mathbb{Z}_2$-SBPT regardless their topology. The paper ends by applying the picture of the dumbbell $Σ_v$'s to a physical model, i.e. the mean-field $ϕ^4$ model.

cond-mat.stat-mech↗

arXiv2011

A simple topological model with continuous phase transition

In the area of topological and geometric treatment of phase transitions and symmetry breaking in Hamiltonian systems, in a recent paper some general sufficient conditions for these phenomena in $\mathbb{Z}_2$-symmetric systems (i.e. invariant under reflection of coordinates) have been found out. In this paper we present a simple topological model satisfying the above conditions hoping to enlighten the mechanism which causes this phenomenon in more general physical models. The symmetry breaking is testified by a continuous magnetization with a nonanalytic point in correspondence of a critical temperature which divides the broken symmetry phase from the unbroken one. A particularity with respect to the common pictures of a phase transition is that the nonanalyticity of the magnetization is not accompanied by a nonanalytic behavior of the free energy.

cond-mat.stat-mech↗

arXiv2007

Two-spin entanglement distribution near factorized states

We study the two-spin entanglement distribution along the infinite $S=1/2$ chain described by the XY model in a transverse field; closed analytical expressions are derived for the one-tangle and the concurrences $C_r$, $r$ being the distance between the two possibly entangled spins, for values of the Hamiltonian parameters close to those corresponding to factorized ground states. The total amount of entanglement, the fraction of such entanglement which is stored in pairwise entanglement, and the way such fraction distributes along the chain is discussed, with attention focused on the dependence on the anisotropy of the exchange interaction. Near factorization a characteristic length-scale naturally emerges in the system, which is specifically related with entanglement properties and diverges at the critical point of the fully isotropic model. In general, we find that anisotropy rule a complex behavior of the entanglement properties, which results in the fact that more isotropic models, despite being characterized by a larger amount of total entanglement, present a smaller fraction of pairwise entanglement: the latter, in turn, is more evenly distributed along the chain, to the extent that, in the fully isotropic model at the critical field, the concurrences do not depend on $r$.

quant-ph↗

arXiv2005

Topological conditions for discrete symmetry breaking and phase transitions

In the framework of a recently proposed topological approach to phase transitions, some sufficient conditions ensuring the presence of the spontaneous breaking of a Z_2 symmetry and of a symmetry-breaking phase transition are introduced and discussed. A very simple model, which we refer to as the hypercubic model, is introduced and solved. The main purpose of this model is that of illustrating the content of the sufficient conditions, but it is interesting also in itself due to its simplicity. Then some mean-field models already known in the literature are discussed in the light of the sufficient conditions introduced here.

cond-mat.stat-mech↗