相关论文: Continuous vs discrete spins in the hyperbolic pla…
We prove that if $E$ is a compact subset of the unit disk ${\mathbb D}$ in the complex plane, if $E$ contains a sequence of distinct points $a_n\not= 0$ for $n\geq 1$ such that $\lim_{n\to\infty} a_n=0$ and for all $n$ we have $ |a_{n+1}|…
We study the phase transition between the high temperature algebraic liquid phase and the low temperature ordered phase in several different types of locally constrained O(N) spin systems, using a unified constrained Ginzburg-Landau…
The hyperbolic plane admits a quasi-isometric embedding into a hyperbolic group if and only if the group is not virtually free.
In conventional spin glasses, magnetic interaction is not strongly anisotropic and the entire spin system is believed to be frozen below the spin-glass transition temperature. In La2Cu0.94Li0.06O4, for which the in-plane exchange…
A relation between O(n) lattice spin models and Ising models defined on the same lattice was recently put forward [L. Casetti, C. Nardini, and R. Nerattini, Phys. Rev. Lett. 106, 057208 (2011)]. Such a relation, inspired by an energy…
We describe a one-parameter family of dispersing (hence hyperbolic, ergodic and mixing) billiards where the correlation function of the collision map decays as $1/n^a$ (here $n$ denotes the discrete time), in which the degree $a \in (1,…
We examine the problem of damage spreading in the off-equilibrium mode coupling equations. The study is done for the spherical $p$-spin model introduced by Crisanti, Horner and Sommers. For $p>2$ we show the existence of a temperature…
Nonlinear theories generalizing Maxwell's electromagnetism and arising from a Lagrangian formalism have dispersion relations in which propagation planes factor into null planes corresponding to two effective metrics which depend on the…
We study the Dirichlet problem for harmonic maps between hyperbolic planes, under the assumption that the Euclidean harmonic extension of the boundary map is quasiconformal.
We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Riemann surface. The continuum theory of these models can be…
We consider $O(n)$-invariant and reflection-positive quantum spin systems on the integer lattice in any dimension, and prove that spin-spin correlations decay exponentially fast provided n is large enough. This answers a question of…
The thermodynamic properties of a one-dimensional model describing spin dynamics in the presence of a twofold orbital degeneracy are studied numerically using the transfer-matrix renormalization group (TMRG). The model contains an…
We study the decoherence of a spin-1/2 induced by an environment which is on the verge of a continuous phase transition. We consider spin environments described by the ferromagnetic and antiferromagnetic Heisenberg models on a square…
We investigate spin correlations in one-dimensional $SU(2)$-invariant Heisenberg chains with exchange disorder for spin lengths $S=1/2$ and $S=1$. In the weak-disorder regime, the eigenmodes of the spin-spin correlation matrix are…
We show that many graphs naturally associated to a connected, compact, orientable surface are hierarchically hyperbolic spaces in the sense of Behrstock, Hagen and Sisto. They also automatically have the coarse median property defined by…
High temperature expansions for the susceptibility and the second correlation moment of the classical N-vector model (also known as the O(N) symmetric Heisenberg classical spin model or the as the lattice O(N) nonlinear sigma model) on the…
Simulations of nematic-isotropic transition of liquid crystals in two dimensions are performed using an O(2) vector model characterised by non linear nearest neighbour spin interaction governed by the fourth Legendre polynomial $P\_4$. The…
A kinetic one-dimensional Ising model on a ring evolves according to a generalization of Glauber rates, such that spins at even (odd) lattice sites experience a temperature $T_{e}$ ($T_{o}$). Detailed balance is violated so that the spin…
We prove the existence of correlations between the equilibrium states at different temperatures of the multi-$p$-spin spherical spin-glass models with continuous replica symmetry breaking: there is no chaos in temperature in these models.…
In systems with a spontaneously broken continuous symmetry, the perturbative loop expansion is plagued with infrared divergences due to the coupling between transverse and longitudinal fluctuations. As a result the longitudinal…