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The universality class of a phase transition is often determined by factors like dimensionality and inherent symmetry. We study the magnetic dipole system in which the ground-state symmetry and the underlying lattice structure are coupled…
The formation of textured patterns has been predicted to occur in two stages. The first is an early time, domain-forming stage with dynamics characterized by a disorder function $\bar\delta (\beta) \sim t^{-\sigma_{E}}$, with $\sigma_{E} =…
An SU(2) lattice gauge theory with two doublets of complex scalar fields is considered. All continuous symmetries are identified and, using the nonperturbative methods of lattice field theory, the phase diagram is mapped out by direct…
We present a mean-field description of the zig-zag phase transition of a quasi-one-dimensional system of strongly interacting particles, with interaction potential $r^{-n}e^{-r/\lambda}$, that are confined by a power-law potential…
We present the phenomenology of the one dimensional non-reciprocal Cahn Hilliard model for varying non-reciprocity $(\alpha)$ and different boundary conditions. At small $\alpha$, a perturbed uniform state evolves to a defect laden…
A cell dynamical system model for deterministic chaos enables precise quantification of the round-off error growth,i.e., deterministic chaos in digital computer realizations of mathematical models of continuum dynamical systems. The model…
Nonreciprocal interactions in many-body systems lead to time-dependent states, commonly observed in biological, chemical, and ecological systems. The stability of these states in the thermodynamic limit and the critical behavior of the…
In the paper a one-dimensional model with nearest - neighbor interactions $I_n, n\in \Z$ and spin values $\pm 1$ is considered. It is known that under some conditions on parameters $I_n$ the phase transition occurs for the model. We define…
The scattering theory of the integrable statistical models can be generalized to the case of systems with extended lines of defect. This is done by adding the reflection and transmission amplitudes for the interactions with the line of…
Experimental systems with a first order phase transition will often exhibit hysteresis when out of equilibrium. If defects are present, the hysteresis loop can have different shapes: with small disorder the hysteresis loop has a macroscopic…
We study the phase-ordering kinetics following a temperature quench of O(N) continuous symmetry models with and 4 on graphs. By means of extensive simulations, we show that the global pattern of scaling behaviours is analogous to the one…
We study two-dimensional Ising spins, evolving through reinforcement learning using their state, action, and reward. The state of a spin is defined as whether it is in the majority or minority with its nearest neighbours. The spin updates…
We study the equilibrium and dynamic phase transition properties of two-dimensional Ising model on a decorated triangular lattice under the influence of a time-dependent magnetic field composed of a periodic square wave part plus a time…
The phase transition occurring in a square 2-D spin lattice governed by an anisotropic Heisenberg Hamiltonian has been studied according to two recently proposed methods. The first one, the Dressed Cluster Method, provides excellent…
The properties of scattering phases in quantum dots are analyzed with the help of lattice models. We first derive the expressions relating the different scattering phases and the dot Green functions. We analyze in detail the Friedel sum…
A spin-1/2 chain model that includes three spin interactions can effectively describe the dynamics of two species of bosons trapped in an optical lattice with a triangular-ladder configuration. A perturbative theoretical approach and…
We investigate the dynamical behaviour of the Ising model under a zero temperature quench with the initial fraction of up spins $0\leq x\leq 1$. In one dimension, the known results for persistence probability are verified; it shows…
In this paper we demonstrate that the phase space arclength of a trajectory, quantified by the time-averaged Lagrangian descriptor, is a robust and self-contained chaos indicator. By invoking Birkhoff's Ergodic Partition Theorem, we show…
For any translation-invariant quantum lattice system with a symmetry group G, we propose a practical and universal construction of order parameters which identify quantum phase transitions with symmetry-breaking order. They are defined in…
The phase diagram of a system of monodispersed hard rectangles of size $m\times m k$ on a square lattice is numerically determined for $m=2,3$ and aspect ratio $k= 1,2,\ldots, 7$. We show the existence of a disordered phase, a nematic phase…