Spatial and structural stability in thermoelasto-dynamics on a half-cylinder

EnThe linear nonhomogeneous thermoelastodynamic problem in a half-cylinder is considered subject to assigned initial conditions, and to the displacement and temperature being specified over the base, and vanishing on the lateral boundary. Spatial stability, derived from a differential inequality, establishes that the mean-square volume integrals of displacement and temperature are bounded above by a decaying function of axial distance for each finite positive time instant. Structural stability, which here relates to continuous dependence of the displacement on the thermal coupling, depends upon the construction of further differential inequalities

Density matrix renormalization group for the Berezinskii-Kosterlitz-Thouless transition of the 19-vertex model

We embody the density matrix renormalization group (DMRG) method for the 19-vertex model on a square lattice in order to investigate the Berezinskii-Kosterlitz-Thouless transition. Elements of the transfer matrix of the 19-vertex model are classified in terms of the total value of arrows in one layer of the square lattice. By using this classification, we succeed to reduce enormously the dimension of the matrix which has to be diagonalized in the DMRG method. We apply our method to the 19-vertex model with the interaction $K=1.0866$ and obtain $c=1.006(1)$ for the conformal anomaly. PACS. 05.90.+m, 02.70.-cComment: RevTeX style, 20 pages, 12 figure

Roughening Induced Deconstruction in (100) Facets of CsCl Type Crystals

The staggered 6-vertex model describes the competition between surface roughening and reconstruction in (100) facets of CsCl type crystals. Its phase diagram does not have the expected generic structure, due to the presence of a fully-packed loop-gas line. We prove that the reconstruction and roughening transitions cannot cross nor merge with this loop-gas line if these degrees of freedom interact weakly. However, our numerical finite size scaling analysis shows that the two critical lines merge along the loop-gas line, with strong coupling scaling properties. The central charge is much larger than 1.5 and roughening takes place at a surface roughness much larger than the conventional universal value. It seems that additional fluctuations become critical simultaneously.Comment: 31 pages, 9 figure

Equilibrium shapes and faceting for ionic crystals of body-centered-cubic type

A mean field theory is developed for the calculation of the surface free energy of the staggered BCSOS, (or six vertex) model as function of the surface orientation and of temperature. The model approximately describes surfaces of crystals with nearest neighbor attractions and next nearest neighbor repulsions. The mean field free energy is calculated by expressing the model in terms of interacting directed walks on a lattice. The resulting equilibrium shape is very rich with facet boundaries and boundaries between reconstructed and unreconstructed regions which can be either sharp (first order) or smooth (continuous). In addition there are tricritical points where a smooth boundary changes into a sharp one and triple points where three sharp boundaries meet. Finally our numerical results strongly suggest the existence of conical points, at which tangent planes of a finite range of orientations all intersect each other. The thermal evolution of the equilibrium shape in this model shows strong similarity to that seen experimentally for ionic crystals.Comment: 14 Pages, Revtex and 10 PostScript figures include

Correlated percolation and the correlated resistor network

We present some exact results on percolation properties of the Ising model, when the range of the percolating bonds is larger than nearest-neighbors. We show that for a percolation range to next-nearest neighbors the percolation threshold Tp is still equal to the Ising critical temperature Tc, and present the phase diagram for this type of percolation. In addition, we present Monte Carlo calculations of the finite size behavior of the correlated resistor network defined on the Ising model. The thermal exponent t of the conductivity that follows from it is found to be t = 0.2000 +- 0.0007. We observe no corrections to scaling in its finite size behavior.Comment: 16 pages, REVTeX, 6 figures include

Two-dimensional O(n) model in a staggered field

Nienhuis' truncated O(n) model gives rise to a model of self-avoiding loops on the hexagonal lattice, each loop having a fugacity of n. We study such loops subjected to a particular kind of staggered field w, which for n -> infinity has the geometrical effect of breaking the three-phase coexistence, linked to the three-colourability of the lattice faces. We show that at T = 0, for w > 1 the model flows to the ferromagnetic Potts model with q=n^2 states, with an associated fragmentation of the target space of the Coulomb gas. For T>0, there is a competition between T and w which gives rise to multicritical versions of the dense and dilute loop universality classes. Via an exact mapping, and numerical results, we establish that the latter two critical branches coincide with those found earlier in the O(n) model on the triangular lattice. Using transfer matrix studies, we have found the renormalisation group flows in the full phase diagram in the (T,w) plane, with fixed n. Superposing three copies of such hexagonal-lattice loop models with staggered fields produces a variety of one or three-species fully-packed loop models on the triangular lattice with certain geometrical constraints, possessing integer central charges 0 <= c <= 6. In particular we show that Benjamini and Schramm's RGB loops have fractal dimension D_f = 3/2.Comment: 40 pages, 17 figure

Monte Carlo simulation of ice models

We propose a number of Monte Carlo algorithms for the simulation of ice models and compare their efficiency. One of them, a cluster algorithm for the equivalent three colour model, appears to have a dynamic exponent close to zero, making it particularly useful for simulations of critical ice models. We have performed extensive simulations using our algorithms to determine a number of critical exponents for the square ice and F models.Comment: 32 pages including 15 postscript figures, typeset in LaTeX2e using the Elsevier macro package elsart.cl

Dynamic Critical Behavior of a Swendsen-Wang-Type Algorithm for the Ashkin-Teller Model

We study the dynamic critical behavior of a Swendsen-Wang-type algorithm for the Ashkin--Teller model. We find that the Li--Sokal bound on the autocorrelation time ($\tau_{{\rm int},{\cal E}} \ge {\rm const} \times C_H$) holds along the self-dual curve of the symmetric Ashkin--Teller model, and is almost but not quite sharp. The ratio $\tau_{{\rm int},{\cal E}} / C_H$ appears to tend to infinity either as a logarithm or as a small power ($0.05 \leq p \leq 0.12$). In an appendix we discuss the problem of extracting estimates of the exponential autocorrelation time.Comment: 59 pages including 3 figures, uuencoded g-compressed ps file. Postscript size = 799740 byte

Two phase transitions in the fully frustrated XYXY model

The fully frustrated $XY$ model on a square lattice is studied by means of Monte Carlo simulations. A Kosterlitz-Thouless transition is found at $T_{\rm KT} \approx 0.446$, followed by an ordinary Ising transition at a slightly higher temperature, $T_c \approx 0.452$. The non-Ising exponents reported by others, are explained as a failure of finite size scaling due to the screening length associated with the nearby Kosterlitz-Thouless transition.Comment: REVTEX file, 8 pages, 5 figures in uuencoded postscrip

Bloch-Wall Phase Transition in the Spherical Model

The temperature-induced second-order phase transition from Bloch to linear (Ising-like) domain walls in uniaxial ferromagnets is investigated for the model of D-component classical spin vectors in the limit D \to \infty. This exactly soluble model is equivalent to the standard spherical model in the homogeneous case, but deviates from it and is free from unphysical behavior in a general inhomogeneous situation. It is shown that the thermal fluctuations of the transverse magnetization in the wall (the Bloch-wall order parameter) result in the diminishing of the wall transition temperature T_B in comparison to its mean-field value, thus favouring the existence of linear walls. For finite values of T_B an additional anisotropy in the basis plane x,y is required; in purely uniaxial ferromagnets a domain wall behaves like a 2-dimensional system with a continuous spin symmetry and does not order into the Bloch one.Comment: 16 pages, 2 figure