Related papers: On the general one-dimensional XY Model: positive …
We generalize several results of the classical theory of Thermodynamic Formalism by considering a compact metric space $M$ as the state space. We analyze the shift acting on $M^\mathbb{N}$ and consider a general a-priori probability for…
We consider $(M,d)$ a connected and compact manifold and we denote by $X$ the Bernoulli space $M^{\mathbb{N}}$. The shift acting on $X$ is denoted by $\sigma$. We analyze the general XY model, as presented in a recent paper by A. T.…
Consider $T(x)= d \, x$ (mod 1) acting on $S^1$, a Lipschitz potential $A:S^1 \to \mathbb{R}$, $0<\lambda<1$ and the unique function $b_\lambda:S^1 \to \mathbb{R}$ satisfying $ b_\lambda(x) = \max_{T(y)=x} \{ \lambda \, b_\lambda(y) +…
We perform Monte Carlo simulations to study the two dimensional random-bond XY model on a square lattice. Two kinds of bond randomness with the coupling coefficient obeying the Gaussian or uniform distribution are discussed. It is shown…
Suppose $\sigma$ is the shift acting on Bernoulli space $X=\{0,1\}^\mathbb{N}$, and, consider a fixed function $f:X \to \mathbb{R}$, under the Waters's conditions (defined in a paper in ETDS 2007). For each real value $t\geq 0$ we consider…
We are interested in the study of Gibbs and equilbrium probabilities on the lattice $\mathbb{R}^{\mathbb{N}}$. Consider the unilateral full-shift defined on the non-compact set $\mathbb{R}^{\mathbb{N}}$ and an $\alpha$-H\"older continuous…
We study the zero-temperature limit of the Gibbs measures of a class of long-range potentials on a full shift of two symbols $\{0,1\}$. These potentials were introduced by Walters as a natural space for the transfer operator. In our case,…
Using the tensor renormalization group method based on the higher-order singular value decom- position, we have studied the thermodynamic properties of the continuous XY model on the square lattice. The temperature dependence of the free…
The temperature inversion symmetry $R\to \frac{1}{T}$ is studied for the finite temperature effective potential of the N=1, $d=5$, supersymmetric $SU(3)_{c}{\times}SU(3)_{w}$ model, on the orbifold $S^{1}/Z_{2}$. For the value of the Wilson…
Consider a compact metric space $(M, d_M)$ and $X = M^{\mathbb{N}}$. We prove a Ruelle's Perron Frobenius Theorem for a class of compact subshifts with Markovian structure introduced in [Bull. Braz. Math. Soc. 45 (2014), pp. 53-72] which…
We demonstrate, with a concrete example, how the combinatorial approach to a general system of particles, which was introduced in detail in the earlier paper arXiv:1205.4986, works and where it enters to provide a genuine extension of…
We analyze some properties of maximizing stationary Markov probabilities on the Bernoulli space $[0,1]^\mathbb{N}$, More precisely, we consider ergodic optimization for a continuous potential $A$, where $A: [0,1]^\mathbb{N}\to \mathbb{R}$…
An $XY$ model, generalized by inclusion of up to an infinite number of higher-order pairwise interactions with an exponentially decreasing strength, is studied by spin-wave theory and Monte Carlo simulations. At low temperatures the model…
The phase transition in the XY model on one-dimensional small-world networks is investigated by means of Monte-Carlo simulations. It is found that long-range order is present at finite temperatures, even for very small values of the…
We discuss the thermodynamics of the O(N) nonlinear sigma model in 1+1 dimensions. In particular we investigate the NLO 1/N correction to the 1PI finite temperature effective potential expressed in terms of an auxiliary field. The effective…
We consider the classical XY model (O(2) nonlinear sigma-model) on a class of lattices with the (fractal) dimensions 1<D<2. The Berezinskii's harmonic approximation suggests that the model undergoes a phase transition in which the low…
We study the magnetic susceptibility of 1D quantum XY model, and show that when the temperature approaches zero, the magnetic susceptibility exhibits the finite-temperature scaling behavior. This scaling behavior of the magnetic…
The exactly solvable model of a one dimensional isotropic XY spin chain is employed to study the thermodynamics of open systems. For this purpose the chain is subdivided into two parts, one part is considered as the system while the rest as…
We exhibit Lipschitz (and hence H\"older) potentials on the full shift $\{0,1\}^{\mathbb{N}}$ such that the associated Gibbs measures fail to converge as the temperature goes to zero. Thus there are "exponentially decaying" interactions on…
We examine the entanglement of thermal states of n spins interacting through different types of XY couplings in the presence of a magnetic field, by evaluating the negativities of all possible bipartite partitions of the whole system and of…