Related papers: A solvable model for symmetry-breaking phase trans…
We study stationary solutions of McKean-Vlasov equations on the circle. Our main contributions stem from observing an exact equivalence between solutions of the stationary McKean-Vlasov equation and an infinite-dimensional quadratic system…
We introduce a one-dimensional two-component system with the self-focusing cubic nonlinearity concentrated at a symmetric set of two spots. Effects of the spontaneous symmetry breaking (SSB) of localized modes were previously studied in the…
We comment on the recent work by Yamaguchi and Barr\'e [Phys. Rev. E 107, 054203 (2023)], which uses linear stability analysis of the Vlasov equation to characterize phase transitions in a generalized Hamiltonian Mean Field (gHMF) model. By…
Within the framework of an exactly solvable model, which takes into account the interaction of fluctuating modes with equal and opposite momenta, we consider phase diagrams in systems with coupled scalar order parameters. We show that, in…
We construct solvable models on the honeycomb lattice by combining three faces of the square lattice solvable models into a hexagon face. These models contain two independent, anisotropy controlling, spectral parameters and their transfer…
In this paper we consider nonlinearly elastic, frame-indifferent, and singularly perturbed two-well models for materials undergoing solid-solid phase transitions in any space dimensions, and we perform a simultaneous passage to…
We investigate the marginally stable modes of the scalar (vector) perturbations in the AdS soliton background coupled to electric field. In the probe limit, we find that the marginally stable modes can reveal the onset of the phase…
The paradigm of second-order phase transitions (PTs) induced by spontaneous symmetry breaking (SSB) in thermal and quantum systems is a pillar of modern physics that has been fruitfully applied to out-of-equilibrium open quantum systems.…
The first analytic topologically non-trivial solutions in the (3+1)-dimensional gauged non-linear sigma model representing multi-solitons at finite volume with manifest ordered structures generating their own electromagnetic field are…
The two-dimensional generalization of the Polyelectolite model of DNA is proposed. It is reduced to the boundary problem for nonlinear completely integrable equation $\sh$-Gordon. In the linearisible version the exact solution is…
Subsystem symmetry has emerged as a powerful organizing principle for unconventional quantum phases of matter, most prominently fracton topological orders. Here, we focus on a special subclass of such symmetries, known as higher-form…
We study a non-Hermitian two-level system with square-wave modulated dissipation and coupling. Based on the Floquet theory, we achieve an effective Hamiltonian from which the boundaries of the $\mathcal{PT}$ phase diagram are captured…
We construct exactly solvable models for a wide class of symmetry enriched topological (SET) phases. Our construction applies to 2D bosonic SET phases with finite unitary onsite symmetry group $G$ and we conjecture that our models realize…
Bifurcation with symmetry is considered in the case of an isotropy subgroup with a two-dimensional fixed point subspace and non-zero quadratic terms. In general, there are one or three branches of solutions, and five qualitatively different…
A semiclassical picture of spontaneous symmetry breaking in light front field theory is formulated. It is based on a finite-volume quantization of self-interacting scalar fields obeying antiperiodic boundary conditions. This choice avoids a…
Canonical analysis has long been the primary analysis method for studies of phase transitions. However, this approach is not sensitive enough if transition signals are too close in temperature space. The recently introduced generalized…
In this paper we consider a class of systems of two coupled real scalar fields in bidimensional spacetime, with the main motivation of studying classical or linear stability of soliton solutions. Firstly, we present the class of systems and…
We study the existence and stability of localized states in the two-dimensional (2D) nonlinear Schrodinger (NLS)/Gross-Pitaevskii equation with a symmetric four-well potential. Using a fourmode approximation, we are able to trace the…
We report branches of explicit expressions for nonlinear modes in parity-time (PT) symmetric potentials of several types. For the single-well and double-well potentials the found solutions are two-parametric and appear to be stable even…
We address one-dimensional soliton formation in the cubic nonlinear medium with two-photon absorption and transversally inhomogeneous gain landscape consisting of a single or several amplifying channels. Existence of the solitons requires…