Zeros of the partition function for a continuum system at first-order transitions

Exact partition function zeros of the Wako-Saitô-Muñoz-Eaton protein model

I compute exact partition function zeros of the Wako-Saitô-Muñoz-Eaton model for various secondary structural elements and for two proteins, 1BBL and 1I6C, by using both analytic and numerical methods. Two-state and barrierless downhill folding transitions can be distinguished by a gap in the distribution of zeros at the positive real axis.

Bimodal behavior of the heaviest fragment distribution in projectile fragmentation

The charge distribution of the heaviest fragment detected in the decay of quasiprojectiles produced in intermediate energy heavy-ion collisions has been observed to be bimodal. This feature is expected as a generic signal of phase transition in nonextensive systems. In this Letter, we present new analyses of experimental data from Au on Au collisions at 60, 80, and 100 MeV/nucleon showing that bimodality is largely independent of the data selection procedure and of entrance channel effects. An estimate of the latent heat of the transition is extracted.

Lee-Yang zeros of periodic and quasiperiodic anisotropic XY chains in a transverse field

The partition function zeros of the anisotropic XY chain in a complex transverse field are studied analytically and numerically. It is found that the partition function zeros of the periodic and quasiperiodic quantum Ising chain lie on the circle at zero temperature and the radius equal to the values of the critical field. For the periodic and quasiperiodic anisotropic XY chains, the closed curves are split to two or three closed curves as the anisotropic parameter gamma decreases at a given ratio of two kinds of exchange interactions. For the isotropic XX case, the partition function zeros lie on the straight segments which are parallel to the real axis and the segments move towards the real axis as the temperature goes to zero.

Transient backbending behavior in the Ising model with fixed magnetization

The physical origin of the backbendings in the equations of state of finite but not necessarily small systems is studied in the Ising model with fixed magnetization (IMFM) by means of the topological properties of the observable distributions and the analysis of the largest cluster with increasing lattice size. Looking at the convexity anomalies of the IMFM thermodynamic potential, it is shown that the order of the transition at the thermodynamic limit can be recognized in finite systems independently of the lattice size. General statistical mechanics arguments and analytical calculations suggest that the backbending in the caloric curve is a transient behavior which should not converge to a plateau in the thermodynamic limit, while the first-order transition (in the Ehrenfest sense) is still signaled by a discontinuity in the magnetization equation of state.

Topology of event distributions as a generalized definition of phase transitions in finite systems

We propose a definition of first order phase transitions in finite systems based on topology anomalies of the event distribution in the space of observations. This generalizes the definitions based on the curvature anomalies of thermodynamical potentials, provides a natural definition of order parameters, and can be related to the Yang-Lee theorem in the thermodynamical limit. It is directly operational from the experimental point of view. It allows to study phase transitions in Gibbs equilibria as well as in other ensembles such as the Tsallis ensemble.

Exact zeros of the partition function for a continuum system with double gaussian peaks

We calculate the exact zeros of the partition function for a continuum system where the probability distribution for the order parameter is given by two asymmetric Gaussian peaks. When the positions of the two peaks coincide, the two separate loci of the zeros that used to give a first-order transition touch each other, with the density of zeros vanishing at the contact point on the positive real axis. Instead of the second-order transition of the Ehrenfest classification as one might naively expect, one finds a critical behavior in this limit.

General theory of lee-yang zeros in models with first-order phase transitions

We present a general, rigorous theory of Lee-Yang zeros for models with first-order phase transitions that admit convergent contour expansions. We derive formulas for the positions and the density of the zeros. In particular, we show that, for models without symmetry, the curves on which the zeros lie are generically not circles, and can have topologically nontrivial features, such as bifurcation. Our results are illustrated in three models in a complex field: the low-temperature Ising and Blume-Capel models, and the q-state Potts model for large q.