Related papers: Zeros of the partition function and dynamical sing…
A mean field spherical model with random couplings between pairs, quartets, and possibly higher multiplets of spins is considered. It has the same critical behavior as the Sherrington-Kirkpatrick model. It thus exhibits replica symmetry…
We study the zeros in the complex plane of the partition function for the Ising model coupled to 2d quantum gravity for complex magnetic field and real temperature, and for complex temperature and real magnetic field, respectively. We…
Lee-Yang zeros are points in the complex plane of an external control parameter at which the partition function vanishes for a many-body system of finite size. In the thermodynamic limit, the Lee-Yang zeros approach the critical value on…
Lee-Yang theory is central to the analysis of thermal phase transitions. However, the underlying mechanism of the theory and the nature of Lee-Yang zeros in quantum many-body systems remains elusive. Here, we develop a unified framework for…
Temperature chaos is an extreme sensitivity of the equilibrium state to a change of temperature. It arises in several disordered systems that are described by the so called scaling theory of spin glasses, while it seems to be absent in mean…
Infinite-range spin-glass models with Levy-distributed interactions show a freezing transition similar to disordered spin systems on finite connectivity random graphs. It is shown that despite diverging moments of the local field…
The statistical mechanics of a two-state Ising spin-glass model with finite random connectivity, in which each site is connected to a finite number of other sites, is extended in this work within the replica technique to study the phase…
The study of spin-glass dynamics, long considered the paradigmatic complex system, has reached important milestones. The availability of single crystals has allowed the experimental measurement of spin-glass coherence lengths of almost…
By using real space renormalisation group (RG) methods we show that spin-glasses in a field display a new kind of transition in high dimensions. The corresponding critical properties and the spin-glass phase are governed by two…
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…
We propose an approach toward understanding the spin glass phase at zero and low temperature by studying the stability of a spin glass ground state against perturbations of a single coupling. After reviewing the concepts of flexibility,…
We present a generalized circle theorem which includes the Lee-Yang theorem for symmetric transitions as a special case. It is found that zeros of the partition function can be written in terms of discontinuities in the derivatives of the…
To simulate indistinguishable particles, recent studies of path-integral molecular dynamics formulated their partition function $Z$ as a recurrence relation involving a variable $\xi$, with $\xi=1$(-1) for bosons (fermions). Inspired by…
Recent developments in study of two-dimensional spin glass models are reviewed in light of fractal nature of droplets at zero-temperature. Also presented are some new results including a new estimate of the stiffness exponent using a…
Infinite-range spin-glass models with Levy-distributed interactions show a spin-glass transition with similarities to both the Sherrington-Kirkpatrick model and to disordered spin systems on finite connectivity random graphs. Despite the…
In a classical work of the 1950's, Lee and Yang proved that the zeros of the partition functions of a ferromagnetic Ising models always lie on the unit circle. Distribution of these zeros is physically important as it controls phase…
In the present paper we analyze the critical properties of a quantum spherical spin glass model with short range, random interactions. Since the model allows for rigorous detailed calculations, we can show how the effective partition…
We analyze the partition function of the Ising model on graphs of two different types: complete graphs, wherein all nodes are mutually linked and annealed scale-free networks for which the degree distribution decays as $P(k)\sim…
We investigate Lee-Yang zeros of generating functions of dynamical observables and establish a general relation between phase transitions in ensembles of trajectories of stochastic many-body systems and the time evolution of high-order…
We investigate the Ising model in one, two, and three dimensions using a cumulant method that allows us to determine the Lee-Yang zeros from the magnetization fluctuations in small lattices. By doing so with increasing system size, we are…