We report on a new method to extract thermodynamic properties from the density of partition function zeroes on finite lattices. This allows direct determination of the order and strength of phase transitions numerically. Furthermore, it enables efficient distinguishing between firstand second-order transitions, elucidates crossover between them and illuminates the origins of finite-size scaling...

The Ising ferromagnet, consisting of magnetic spins, is the simplest system showing phase transitions and critical phenomena at finite temperatures. The Ising ferromagnet has played a central role in our understanding of phase transitions and critical phenomena. Also, the Ising ferromagnet explains the gas-liquid phase transitions accurately. In particular, the Ising ferromagnet in a nonzero ma...

We demonstate the existence of a large N phase transition with respect to the ’t Hooft coupling in q-deformed Yang-Mills theory on S2. The strong coupling phase is characterized by the formation of a clump of eigenvalues in the associated matrix model of the Douglas-Kazakov (DK) type [1]. By understanding this in terms of instanton contributions to the q-deformed Yang-Mills theory, we gain some...

Partition coefficients of hydrophilic organic solvents (C1-C5 acetate esters and alcohols) in distilled water, olive oil, human blood, and various rat tissues (blood, liver, kidney, brain, muscle, and fat) were determined. Water/air partition coefficients were measured by a new vial equilibration technique, which needs no direct measurement of the concentration in either the liquid phase or the...

We explore connections between the phenomenon of correlation decay (more precisely, strong spatial mixing) and location Lee--Yang Fisher zeros for various spin systems. In particular we show that, in many instances, proofs showing that weak mixing on Bethe lattice (infinite $\Delta$-regular tree) implies all graphs maximum degree $\Delta$ can be lifted to complex plane, establishing absence ass...

The nature of the phase transition in the lattice Gross-Neveu model with Wilson fermions is investigated using a new analytical technique. This involves a new type of weak coupling expansion which focuses on the partition function zeroes of the model. Its application to the single flavour Gross-Neveu model yields a phase diagram whose structure is consistent with that predicted from a saddle po...

We construct and study an extended random matrix model of RNA (polymer) folding. A perturbation which acts on all the nucleotides in the chain is added to the action of the RNA partition function. The effect of this perturbation on the partition function and the Genus Distributions is studied. This perturbation distinguishes between the paired and unpaired bases. For example, for α = 1 (where α...