Related papers: Geometry and Dynamics in Zero Temperature Statisti…
We study the dynamical behavior of a lattice model of glass former on a random graph, where no corrections to the mean field description are expected. We find that the behavior of dynamical correlation functions and dynamical susceptibility…
The magnetization dynamics of the triangular lattice of Ising spin chains is investigated in the framework of a two-dimensional model. The rigid chains are assumed to interact with the nearest neighboring chains, an external magnetic field,…
We study the exact statistical mechanics of Lam\'e solitons using a transfer matrix method. This requires a knowledge of the first forbidden band of the corresponding Schr\"odinger equation with the periodic Lam\'e potential. Since the…
Via Monte Carlo studies of the frustrated XY or classical planar model we demonstrate the possibility of a finite (nonzero) temperature spin/gauge glass phase in two dimensions. Examples of both periodic and quasiperiodic two dimensional…
When a liquid freezes, a change in the local atomic structure marks the transition to the crystal. When a liquid is cooled to form a glass, however, no noticeable structural change marks the glass transition. Indeed, characteristic features…
I define a statistical model of graphs in which 2-dimensional spaces arise at low temperature. The configurations are given by graphs with a fixed number of edges and the Hamiltonian is a simple, local function of the graphs. Simulations…
In order to understand the mechanisms for glassy dynamics in biological tissues and shed light on those in non-biological materials, we study the low-temperature disordered phase of 2D vertex-like models. Recently it has been noted that…
Spin-glass systems are universal models for representing many-body phenomena in statistical physics and computer science. High quality solutions of NP-hard combinatorial optimization problems can be encoded into low energy states of…
The purpose of this manuscript is to review my recent activity on three main research topics. The first concerns the nature of low temperature amorphous solids and their relation with the spin glass transition in a magnetic field. This is…
Several authors have recently been studying the equilibrium or KMS states on the Toeplitz algebras of finite higher-rank graphs. For graphs of rank one (that is, for ordinary directed graphs), there is a natural dynamics obtained by lifting…
The dynamical behavior of a kind of models with hierarchically constrained dynamics is investigated. The models exhibit many properties resembling real structural glasses. In particular, we focus on the study of time-dependent temperature…
We consider generalized zero-temperature Glauber dynamics under partially synchronous updating mode for a one dimensional system. Using Monte Carlo simulations, we calculate the phase diagram and show that the system exhibits phase…
By applying a recently proposed mapping, we derive exactly the upper phase boundary of several Ising spin glass models defined over static graphs and random graphs, generalizing some known results and providing new ones.
Isoradial graphs are a natural generalization of regular graphs which give, for many models of statistical mechanics, the right framework for studying models at criticality. In this survey paper, we first explain how isoradial graphs…
Motivated by the concept of geometrical frustration, we introduce a class of statistical mechanics lattice models for the glass transition. Monte Carlo simulations in three dimensions show that they display a dynamical glass transition…
Real-world social and economic networks typically display a number of particular topological properties, such as a giant connected component, a broad degree distribution, the small-world property and the presence of communities of densely…
There is a deep and interesting connection between the topological properties of a graph and the behaviour of the dynamical system defined on it. We analyse various kind of graphs, with different contrasting connectivity or degree…
This is the first installment of a paper in three parts, where we use noncommutative geometry to study the space of commensurability classes of Q-lattices and we show that the arithmetic properties of KMS states in the corresponding quantum…
Three different vortex glass models are studied by examining the energy barrier against vortex motion across the system. In the two-dimensional gauge glass this energy barrier is found to increase logarithmically with system size which is…
A simple and computationally efficient algorithm enables implementing negative temperature values in a spin dynamics simulation. The algorithm uses a Langevin spin dynamics thermostat with a negative damping parameter, enabling the…