Finite-temperature properties of frustrated classical spins coupled to the lattice

We present extensive Monte Carlo simulations for a classical antiferromagnetic Heisenberg model with both nearest ($J_1$) and next-nearest ($J_2$) exchange couplings on the square lattice coupled to the lattice degrees of freedom. The Ising-like phase transition, that appears for $J_2/J_1>1/2$ in the pure spin model, is strengthened by the spin-lattice coupling, and is accompanied by a lattice deformation from a tetragonal symmetry to an orthorhombic one. Evidences that the universality class of the transition does not change with the inclusion of the spin-lattice coupling are reported. Implications for ${\rm Li_2VOSiO_4}$, the prototype for a layered $J_1{-}J_2$ model in the collinear regime, are also discussed.Comment: 6 pages and 8 figure

Ising transition driven by frustration in a 2D classical model with SU(2) symmetry

We study the thermal properties of the classical antiferromagnetic Heisenberg model with both nearest ($J_1$) and next-nearest ($J_2$) exchange couplings on the square lattice by extensive Monte Carlo simulations. We show that, for $J_2/J_1 > 1/2$, thermal fluctuations give rise to an effective $Z_2$ symmetry leading to a {\it finite-temperature} phase transition. We provide strong numerical evidence that this transition is in the 2D Ising universality class, and that $T_c\to 0$ with an infinite slope when $J_2/J_1\to 1/2$.Comment: 4 pages with 4 figure

Topological regularization and self-duality in four-dimensional anti-de Sitter gravity

It is shown that the addition of a topological invariant (Gauss-Bonnet term) to the anti-de Sitter (AdS) gravity action in four dimensions recovers the standard regularization given by holographic renormalization procedure. This crucial step makes possible the inclusion of an odd parity invariant (Pontryagin term) whose coupling is fixed by demanding an asymptotic (anti) self-dual condition on the Weyl tensor. This argument allows to find the dual point of the theory where the holographic stress tensor is related to the boundary Cotton tensor as $T_{j}^{i}=\pm (\ell ^{2}/8\pi G)C_{j}^{i}$, which has been observed in recent literature in solitonic solutions and hydrodynamic models. A general procedure to generate the counterterm series for AdS gravity in any even dimension from the corresponding Euler term is also briefly discussed.Comment: 13 pages, no figures; enlarged discussion on self-duality condition for AAdS spacetimes, references added, final version for PR