Formation of topological defects in first order phase transitions

Journal of Physics A: Mathematical and Theoretical

The investigation of the Hamiltonian dynamical counterpart of phase transitions, combined with the Riemannian geometrization of Hamiltonian dynamics, has led to a preliminary formulation of a differential-topological theory of phase transitions. In fact, in correspondence of a phase transition there are peculiar geometrical changes of the mechanical manifolds that are found to stem from changes of their topology. These findings, together with two theorems, have suggested that a topological theory of phase transitions can be formulated to go beyond the limits of the existing theories. Among other advantages, the new theory applies to phase transitions in smallNsystems (that is, at nanoscopic and mesoscopic scales), and in the absence of symmetry-breaking. However, the preliminary version of the theory was incomplete and still falsifiable by counterexamples. The present work provides a relevant leap forward leading to an accomplished development of the topological theory of phase tran...

Pramana, 1999

In this talk we discuss a new mechanism of formation of topological defects due to enhanced magnitude oscillations of a complex scalar order-parameter (OP) field during bubble collisions in a first order phase transition.

2017

The topological theory of phase transitions was proposed on the basis of different arguments, the most important of which are: a direct evidence of the relation between topology and phase transitions for some exactly solvable models; an explicit relation between entropy and topological invariants of certain submanifolds of configuration space, and, finally, two theorems stating that, for a wide class of physical systems, phase transitions should necessarily stem from topological changes of some submanifolds of configuration space. It has been recently shown that the 2D lattice ϕ^4-model provides a counterexample that falsifies the mentioned theorems. On the basis of a numerical investigation, the present work indicates the way to overcome this difficulty: in spite of the absence of critical points of the potential in correspondence of the transition energy, the phase transition of this model stems from an asymptotic (N→∞) change of topology of the energy level sets.

arXiv: Statistical Mechanics, 2014

The topological theory of phase transitions has its strong point in two theorems proving that, for a wide class of physical systems, phase transitions necessarily stem from topological changes of some submanifolds of configuration space. It has been recently argued that the $2D$ lattice $\phi^4$-model provides a counterexample that falsifies this theory. It is here shown that this is not the case: the phase transition of this model stems from an asymptotic ($N\to\infty$) change of topology of the energy level sets, in spite of the absence of critical points of the potential in correspondence of the transition energy.

Physical Review B

Topological phase transitions can be described by the theory of critical phenomena and identified by critical exponents that define their universality classes. This is a consequence of the existence of a diverging length at the transition that has been identified as the penetration depth of the surface modes in the non-trivial topological phase. In this paper, we characterize different universality classes of topological transitions by determining their correlation length exponents directly from numerical calculations of the penetration length of the edge modes as a function of the distance to the topological transition. We consider generalizations of the topological non-trivial Su-Schriefer-Heeger (SSH) model, for the case of next next nearest neighbors hopping terms and in the presence of a synthetic potential. The latter allows the system to transit between two universality classes with different correlation length and dynamic critical exponents. It presents a line of multi-critical point in its phase diagram since the behavior of the Berry connection depends on the path it is approached. We compare our results with those obtained from a scaling approach to the Berry connection.

Physical Review Letters, 2016

When traversing a symmetry breaking second order phase transition at a finite rate, topological defects form whose number dependence on the quench rate is given by simple power laws. We propose a general approach for the derivation of such scaling laws that is based on the analytical transformation of the associated equations of motion to a universal form rather than employing plausible physical arguments. We demonstrate the power of this approach by deriving the scaling of the number of topological defects in both homogeneous and non-homogeneous settings. The general nature and extensions of this approach are discussed.

Basics and Highlights in Fundamental Physics - Proceedings of the International School of Subnuclear Physics, 2001

Physical Review E - PHYS REV E, 1996

We have investigated the time evolution of a vectorial model C system following a temperature quench from the disordered state into the order-disorder coexistence region, with numerical Langevin simulations. The system is characterized by a vectorial, nonconserved order parameter coupled to a conserved quantity such as a concentration. Two different ordering mechanisms are observed. If the mean concentration co is co>1/2, then the minority phase is the ordered phase and growth is driven by long-range diffusion. On the other hand, if co<1/2, then it is the disordered phase that is in the minority. In this case, defects of the order parameter (vortices) are strongly coupled to that of the position of the disordered phase. Growth takes place primarily via the diffusion and coalescence of the defects, giving rise to an n=1/4 growth exponent over a significant time regime.

Journal of Physics A: Mathematical and General, 2006

We investigate the mechanism by which topological defects form in first order phase transitions with a charged order parameter. We show how thick superconductor vortices and heavy cosmic strings form by trapping of magnetic flux. In an external magnetic field, intermediate objects such as strips and membranes of magnetic flux and chains of single winding defects are produced. At non-zero temperature, a variety of spontaneous defects of different winding numbers arise. In cosmology, our results mean that the magnetic flux thermal fluctuations get trapped in a primordial multi-tension string network. The mechanism may also apply to the production of cosmic-like strings in brane collisions. In a thin type-I superconductor film, flux strips are found to be meta-stable while thick vortices are stable up to some critical value of the winding number which increases with the thickness of the film. In addition, a non-dissipative Josephson-like current is obtained across the strips of quantized magnetic flux.

Physical Review E, 2005