Related papers: XY model in small-world networks
We analyze the non-equilibrium order-disorder transition of Axelrod's model of social interaction in several complex networks. In a small world network, we find a transition between an ordered homogeneous state and a disordered state. The…
Effective theories for random critical points are usually non-unitary, and thus may contain relevant operators with negative scaling dimensions. To study the consequences of the existence of negative dimensional operators, we consider the…
One-dimensional model of a system where first-order phase transition occurs is examined in the present paper. It is shown that basic properties of the phenomenon, such as a well defined temperature of transition, are caused both by…
The two-component cold atom systems with anisotropic hopping amplitudes can be phenomenologically described by a two-dimensional Ising-XY coupled model with spatial anisotropy. At low temperatures, theoretical predictions [Phys. Rev. A 72,…
The two-dimensional dissipative quantum XY model is applicable to the quantum-critical properties of diverse experimental systems, ranging from the superconductor to insulator transitions, ferromagnetic and antiferromagnetic transitions in…
We study the behavior of the classical XY model on a two-dimensional square lattice, with interactions occurring within a vision cone of each spin. Via Monte Carlo simulations, we explore one non-reciprocal and two reciprocal…
We study two versions of the XY model where the spins but also the interaction topology is allowed to change. In the free XY model, the number of links is fixed, but their positions in the network are not. We also study a more relaxed…
We numerically study the critical behavior of the one-dimensional XY model of the size N with variable interaction range L. As expected, the standard local order parameter of the magnetization is shown to well detect the mean-field type…
We have studied the phase transition of the contact process near a multiple junction of $M$ semi-infinite chains by Monte Carlo simulations. As opposed to the continuous transitions of the translationally invariant ($M=2$) and semi-infinite…
The two-dimensional random gauge \xy model, where the quenched random variables are magnetic bond angles uniformly distributed within $[-r\pi, r\pi]$ ($0 \leq r \leq 1$), is studied via Monte Carlo simulations. We investigate the phase…
By combining different ideas, a general and efficient protocol to deal with discontinuous phase transitions at low temperatures is proposed. For small $T$'s, it is possible to derive a generic analytic expression for appropriate order…
We investigate the one-dimensional finite-size XY model with opposing surface fields in the X direction. Exact solutions are obtained for the two-site and three-site models, while numerical methods are employed for models with more than…
Critical behavior of the two-dimensional generalized $XY$ model involving solely nematic-like terms of the second, third and fourth orders is studied by Monte Carlo method. We find that such a system can undergo three successive phase…
The two-dimensional (2D) XY model plays a crucial role in statistical and condensed matter physics. With the introduction of long-range interactions, the system exhibits a richer set of physical phenomena and a crossover between…
The phenomenon of phase transitions in one-dimensional systems is discussed. Equilibrium systems are reviewed and some properties of an energy function which may allow phase transitions and phase ordering in one dimension are identified. We…
Using Monte Carlo methods, the short-time dynamic scaling behaviour of two-dimensional critical XY systems is investigated. Our results for the XY model show that there exists universal scaling behaviour already in the short-time regime,…
Machine learning has become a useful tool for studying phase transitions in statistical systems.For the two-dimensional classical XY model, however, the topological character of the Berezinskii-Kosterlitz-Thouless (BKT) transition and…
The intermediate 3D XY scaling theory of superconductivity at zero and nonzero magnetic fields is developed, based only upon the dimensional hypothesis $B\sim (Length)^{-2}$. Universal as well as nonuniversal aspects of the theory are…
We present extensive Monte Carlo simulations on a two-dimensional XY model with a modified form of interaction potential. Thermodynamic quantities other than energy, specific heat etc (such as magnetization, susceptibility, fourth order…
Large-scale Monte Carlo simulations, together with scaling, are used to obtain the critical behavior of the Hastings long-range model and two corresponding models based on small-world networks. These models have combined short- and…