Related papers: Vertex Models and Random Labyrinths: Phase Diagram…
The dynamic phase diagram of vortex lattices driven in disorder is calculated in two and three dimensions. A modified Lindemann criterion for the fluctuations of the distance of neighboring vortices is used, which unifies previous analytic…
We show that topological phases include disordered materials if the underlying invariant is interpreted as originating from coarse geometry. This coarse geometric framework, grounded in physical principles, offers a natural setting for the…
A system of two self and mutual interacting ring polymers, close together in space, can display several competing equilibrium phases and phase transitions. Using Monte Carlo simulations and combinatorial arguments on a corresponding lattice…
Inspired by the stable bilayer water ice grown in the laboratory (Nature 577, 60, 2020), we propose a model representing water ice as a two-layer six-vertex model. Using the loop update Monte Carlo method, we unveil meaningful findings.…
The article is devoted to the results of a phase topology research on a generalized mathematical model, which covers such two problems as dynamics of two point vortices enclosed in a harmonic trap in a Bose-Einstein condensate and dynamics…
We revisit the phase diagram of Rokhsar-Kivelson models, which are used in fields such as superconductivity, frustrated magnetism, cold bosons, and the physics of Josephson junction arrays. From an extended height effective theory, we show…
We consider an Ising competitive model defined over a triangular Husimi tree where loops, responsible for an explicit frustration, are even allowed. After a critical analysis of the phase diagram, in which a ``gas of non interacting dimers…
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…
This paper introduces a new systematic algorithm for constructing periodic Euclidean weaving diagrams with combinatorial arguments. It is shown that such a weaving diagram can be considered as a specific type of four-regular periodic planar…
The square ice is a canonical example of a Coulomb phase in two dimensions: Its ground state is extensively degenerate and satisfies a local constraint on the spin arrangement (the so-called ice rule). In this paper, we use a loop flip…
We point out some problems with the previously-proposed phase diagram of the $Z_6$ spin models. Consideration of the diagram near to the decoupling surface using both exact and approximate arguments suggests a modification which remedies…
We present the phase diagram and critical properties of a coupled $XY$-Ising model on a triangular lattice using the mean-field approximation, the Migdal-Kadanoff scheme of renormalization group and Monte-Carlo simulations. The topology of…
We propose a model describing liquid-solid phase coexistence in mixed lipid membranes by including explicitly the occurrence of a rippled phase. For a single component membrane, we employ a previous model in which the membrane thickness is…
The phase diagram of a vertex model introduced by P. Di Francesco (Nucl. Phys. B 525, 507 1998) representing the configurations of a square lattice which can fold with different bending energies along the main axes and the diagonals has…
Phase boundaries in p-T and p-V diagrams are essential in material science researches. Exact analytic knowledge about such phase boundaries are known so far only in two-dimensional (2D) Ising-like models, and only for cases with two phases.…
I review recent work on the ``phase diagram'' of the one-dimensional complex Ginzburg-Landau equation for system sizes at which chaos is extensive. Particular attention is paid to a detailed description of the spatiotemporally disordered…
Based on numerical simulation and local stability analysis we describe the structure of the phase space of the edge/triangle model of random graphs. We support simulation evidence with mathematical proof of continuity and discontinuity for…
Models of interacting Majorana modes may be realized in vortex lattices in superconducting films in contact with topological insulators and may be tuned to the strong-interaction regime by adjusting the chemical potential. Extending the…
Phase diagram of a discrete counterpart of the classical Heisenberg model, the truncated tetrahedral model, is analyzed on the square lattice, when the interaction is ferromagnetic. Each spin is represented by a unit vector that can point…
We study a model of colored multiwebs, which generalizes the dimer model to allow each vertex to be adjacent to \(n_v\) edges. These objects can be formulated as a random tiling of a graph with partial dimer covers. We examine the case of a…