Related papers: Zeros of the partition function and dynamical sing…
As a foundation of statistical physics, Lee and Yang in 1952 proved that the partition functions of thermal systems can be zero at certain points (called Lee-Yang zeros) on the complex plane of temperature. In the thermodynamic limit, the…
We show that, at the critical temperature, there is a class of Lee-Yang zeros of the partition function in a general scalar field theory, which location scales with the size of the system with a characteristic exponent expressed in terms of…
Statistical physics provides the concepts and methods to explain the phase behavior of interacting many-body systems. Investigations of Lee-Yang zeros --- complex singularities of the free energy in systems of finite size --- have led to a…
The complex zeros of partition functions were originally investigated by Lee and Yang to explain the behavior of condensing gases. Since then, Lee-Yang zeros have become a powerful tool to describe phase transitions in interacting systems.…
The study of zeros of partition functions, initiated by Yang and Lee, provides an important qualitative and quantitative tool in the study of critical phenomena. This has frequently been used for periodic as well as hierarchical lattices.…
Zeros of the moment of the partition function $[Z^n]_{\bm{J}}$ with respect to complex $n$ are investigated in the zero temperature limit $\beta \to \infty$, $n\to 0$ keeping $y=\beta n \approx O(1)$. We numerically investigate the zeros of…
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 for complex temperature. We compute the zeros by using the exact solution coming from a two…
We discuss the problem of static chaos in spin glasses. In the case of magnetic field perturbations, we propose a scaling theory for the spin-glass phase. Using the mean-field approach we argue that some pure states are suppressed by the…
Lee-Yang theory, based on the study of zeros of the partition function, is widely regarded as a powerful and complimentary approach to the study of critical phenomena and forms a foundational part of the theory of phase transitions. Its…
We study temperature chaos in a two-dimensional Ising spin glass with random quenched bimodal couplings, by an exact computation of the partition functions on large systems. We study two temperature correlators from the total free energy…
In this topical review we discuss the nature of the low-temperature phase in both infinite-ranged and short-ranged spin glasses. We analyze the meaning of pure states in spin glasses, and distinguish between physical, or ``observable'',…
The properties of discrete two-dimensional spin glasses depend strongly on the way the zero-temperature limit is taken. We discuss this phenomenon in the context of the Migdal-Kadanoff renormalization group. We see, in particular, how these…
Phase transitions are typically accompanied by non-analytic behaviors of the free energy, which can be explained by considering the zeros of the partition function in the complex plane of the control parameter and their approach to the…
A new method to extract the density of partition function zeroes (a continuous function) from their distribution for finite lattices (a discrete data set) is presented. This allows direct determination of the order and strength of phase…
The ground-state phase diagram of an Ising spin-glass model on a random graph with an arbitrary fraction $w$ of ferromagnetic interactions is analysed in the presence of an external field. Using the replica method, and performing an…
This paper is divided into two parts. The first part concerns several standard scenarios for how short-range spin glasses might behave at low temperature. Earlier theorems of the authors are reviewed, and some new results presented,…
The Lee-Yang property of a given spin model means that its partition function has purely imaginary zeros as a function of an external magnetic field. A similar property is also used in the theory of quantum anharmonic crystals and quantum…
The two-time correlation function for probe spin interacting with spin system (bath) is studied. We show that zeros of this function correspond to zeros of partition function of spin system in complex magnetic field. The obtained relation…
Spin glasses are the paradigm of complex systems. These materials present really slow dynamics. However, the nature of the spin glass phase in finite dimensional systems is still controversial. Different theories describing the low…
The magnetic systems with disorder form an important class of systems, which are under intensive studies, since they reflect real systems. Such a class of systems is the spin glass one, which combines randomness and frustration. The…