Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userPhase transitions in swarming systems: A recent debate
145
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In this work we consider the phase transition from ordered to disordered states that occur in the Vicsek model of self-propelled particles. This model was proposed to describe the emergence of collective order in swarming systems. When noise is added to the motion of the particles, the onset of collective order occurs through a dynamical phase transition. Based on their numerical results, Vicsek and his colleagues originally concluded that this phase transition was of second order (continuous). However, recent numerical evidence seems to indicate that the phase transition might be of first order (discontinuous), thus challenging Vicseks original results. In this work we review the evidence supporting both aspects of this debate. We also show new numerical results indicating that the apparent discontinuity of the phase transition may in fact be a numerical artifact produced by the artificial periodicity of the boundary conditions.
rate research
Read More
(abridged) In this paper, we present the issues we consider as essential as far as the statistical mechanics of finite systems is concerned. In particular, we emphasis our present understanding of phase transitions in the framework of information theory. Information theory provides a thermodynamically-consistent treatment of finite, open, transient and expanding systems which are difficult problems in approaches using standard statistical ensembles. As an example, we analyze is the problem of boundary conditions, which in the framework of information theory must also be treated statistically. We recall that out of the thermodynamical limit the different ensembles are not equivalent and in particular they may lead to dramatically different equation of states, in the region of a first order phase transition. We recall the recent progresses achieved in the understanding of first-order phase transition in finite systems: the equivalence between the Yang-Lee theorem and the occurrence of bimodalities in the intensive ensemble and the presence of inverted curvatures of the thermodynamic potential of the associated extensive ensemble.
In this paper we study phase transitions for weakly interacting multiagent systems. By investigating the linear response of a system composed of a finite number of agents, we are able to probe the emergence in the thermodynamic limit of a singular behaviour of the susceptibility. We find clear evidence of the loss of analyticity due to a pole crossing the real axis of frequencies. Such behaviour has a degree of universality, as it does not depend on either the applied forcing nor on the considered observable. We present results relevant for both equilibrium and nonequilibrium phase transitions by studying the Desai-Zwanzig and Bonilla-Casado-Morillo models.
We investigate dynamical quantum phase transitions in disordered quantum many-body models that can support many-body localized phases. Employing $l$-bits formalism, we lay out the conditions for which singularities indicative of the transitions appear in the context of many-body localization. Using the combination of the mapping onto $l$-bits and exact diagonalization results, we explicitly demonstrate the presence of these singularities for a candidate model that features many-body localization. Our work paves the way for understanding dynamical quantum phase transitions in the context of many-body localization, and elucidating whether different phases of the latter can be detected from analyzing the former. The results presented are experimentally accessible with state-of-the-art ultracold-atom and ion-trap setups.
We study by Monte Carlo simulations the effect of quenched orientational disorder in systems of interacting classical dipoles on a square lattice. Each dipole can lie along any of two perpendicular axes that form an angle psi with the principal axes of the lattice. We choose psi at random and without bias from the interval [-Delta, Delta] for each site of the lattice. For 0<Delta <~ pi/4 we find a thermally driven second order transition between a paramagnetic and a dipolar antiferromagnetic order phase and critical exponents that change continously with Delta. Near the case of maximum disorder Delta ~ pi/4 we still find a second order transition at a finite temperature T_c but our results point to weak instead of {it strong} long-ranged dipolar order for temperatures below T_c.
When a second-order phase transition is crossed at fine rate, the evolution of the system stops being adiabatic as a result of the critical slowing down in the neighborhood of the critical point. In systems with a topologically nontrivial vacuum manifold, disparate local choices of the ground state lead to the formation of topological defects. The universality class of the transition imprints a signature on the resulting density of topological defects: It obeys a power law in the quench rate, with an exponent dictated by a combination of the critical exponents of the transition. In inhomogeneous systems the situation is more complicated, as the spontaneous symmetry breaking competes with bias caused by the influence of the nearby regions that already chose the new vacuum. As a result, the choice of the broken symmetry vacuum may be inherited from the neighboring regions that have already entered the new phase. This competition between the inherited and spontaneous symmetry breaking enhances the role of causality, as the defect formation is restricted to a fraction of the system where the front velocity surpasses the relevant sound velocity and phase transition remains effectively homogeneous. As a consequence, the overall number of topological defects can be substantially suppressed. When the fraction of the system is small, the resulting total number of defects is still given by a power law related to the universality class of the transition, but exhibits a more pronounced dependence on the quench rate. This enhanced dependence complicates the analysis but may also facilitate experimental test of defect formation theories.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
