Folding transitions of the square--diagonal two--dimensional lattice

We consider the procedure for calculating the pair correlation function in the context of the Cluster Variation Methods. As specific cases, we study the pair correlation function in the paramagnetic phase of the Ising model with nearest neighbors, next to the nearest neighbors and plaquette interactions in two and three dimensions. In presence of competing interactions, the so called disorder line separates in the paramagnetic phase a region where the correlation function has...

We compute the structure factor of the $J_1$-$J_2$ Ising model in an external field on the square lattice within the Cluster Variation Method. We use a four point plaquette approximation, which is the minimal one able to capture phases with broken orientational order in real space, like the recently reported Ising-nematic phase in the model. The analysis of different local maxima in the structure factor allows us to track the different phases and phase transitions against tem...

We report the status of a high-statistics Monte Carlo simulation of non-self-avoiding crystalline surfaces with extrinsic curvature on lattices of size up to $128^2$ nodes. We impose free boundary conditions. The free energy is a gaussian spring tethering potential together with a normal-normal bending energy. Particular emphasis is given to the behavior of the model in the cold phase where we measure the decay of the normal-normal correlation function.

In the present Letter we discuss the origin of the vertex population inversion observed experimentally in the mediated Artificial Square Ice. An interaction modifier is a disc-shaped magnetic nanoisland (a dot) which is placed at the center of a vertex to mediate the interaction between the nearby islands. We show that the inversion is of entropic origin, and can be explained via the renormalization of the vertex configuration energies due to local interaction between the n...

We study by Monte Carlo simulations and scaling analysis two models of pairs of confined and dense ring polymers in two dimensions. The pair of ring polymers are modelled by squared lattice polygons confined within a square cavity and they are placed in relation to each other to be either unlinked or linked in the plane. The observed rich phase diagrams of the two models reveal several equilibrium phases separated by first order and continuous phase boundaries whose critical ...

In this paper we study the phase diagram of the five-state Potts antiferromagnet on the bisected-hexagonal lattice. This question is important since Delfino and Tartaglia recently showed that a second-order transition in a five-state Potts antiferromagnet is allowed, and the bisected-hexagonal lattice had emerged as a candidate for such a transition on numerical grounds. By using high-precision Monte Carlo simulations and two complementary analysis methods, we conclude that t...

The folding of the triangular lattice embedded in two dimensions (discrete planar folding) is investigated numerically. As the bending rigidity K varies, the planar folding exhibits a series of crumpling transitions at K \approx -0.3 and K \approx 0.1. By means of the transfer-matrix method for the system sizes L \le 14, we analyze the singularity of the transition at K \approx -0.3. As a result, we estimate the transition point and the latent heat as K=-0.270(2) and Q=0.043(...

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 to one of the 12 vertices of the truncated tetrahedron, which is a continuous interpolation between the tetrahedron and the octahedron. Phase diagram of the model is determined by means of the statistical analogue of the entanglement entropy...

We use the cluster variation method (CVM) to investigate the phase structure of the 3d gonihedric Ising actions defined by Savvidy and Wegner. The geometrical spin cluster boundaries in these systems serve as models for the string worldsheets of the gonihedric string embedded in ${\bf Z}^3$. The models are interesting from the statistical mechanical point of view because they have a vanishing bare surface tension. As a result the action depends only on the angles of the discr...

We present some illustrations for the claim that already by looking at the ground states of classical lattice models, one may meet some interesting and non-trivial structures.