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Phase transitions of first and second order can easily be distinguished in small systems in the microcanonical ensemble. Configurations of phase coexistence, which are suppressed in the canonical formulation, carry important information…

The scaling theory of critical phenomena has been successfully extended for classical first order transitions even though the correlation length does not diverge in these transitions. In this paper we apply the scaling ideas to quantum…

Using Monte Carlo histogram methods, the microcanonical caloric curve is computed for the Ising model in two and three dimensions with fixed magnetization. Whereas the signatures of a first order phase transition are clearly visible for…

The most important recent results in the theory of phase transitions and quantum effects in quantum anharmonic crystals are presented and discussed. In particular, necessary and sufficient conditions for a phase transition to occur at some…

Here we first develop the thermodynamics of microcanonical phase transitions of first and second order in systems which are thermodynamically stable in the sense of van Hove. We show how both kinds of phase transitions can unambiguously be…

Systems with long range interactions in general are not additive, which can lead to an inequivalence of the microcanonical and canonical ensembles. The microcanonical ensemble may show richer behavior than the canonical one, including…

A first order phase transition is found in a model which was introduced originally by Murthy and Shankar [Phys. Rev. B 60, 6517 (1999)] to describe systems of generalised exclusion statistics. I characterise the phase transition in the…

The dynamics of first order phase transitions are studied in the context of (3+1)-dimensional scalar field theories. Particular attention is paid to the question of quantifying the strength of the transition, and how `weak' and `strong'…

The dynamics of weak vs. strong first order phase transitions is investigated numerically for 2+1 dimensional scalar field models. It is argued that the change from a weak to a strong transition is itself a (second order) phase transition,…

Microcanonical thermodynamics (MT) is analysed for phase transitions of first and second order in finite systems. The transiton temperature, the latent heat and the surface tension of first order transitions can easily be determined by MT…

Electroweak baryogenesis may solve one of the most fundamental questions we can ask about the universe, that of the origin of matter. It has become clear in the past few years that it also poses a multi-faceted challenge. In order to…

By combining different ideas, a general and efficient protocol to deal with discontinuous phase transitions at low temperatures is proposed. For small $T$'s, it is possible to derive a generic analytic expression for appropriate order…

First-order phase transitions exist in many models beyond the Standard Model and can generate detectable stochastic gravitational waves for a strong one. Using the cosmological observables in big bang nucleosynthesis and cosmic microwave…

A microcanonical first order transition, connecting a clustered to a homogeneous phase, is studied from both the thermodynamic and dynamical point of view for a N-body Hamiltonian system with infinite-range couplings. In the microcanonical…

This paper reviews a number of fundamental connections that exist between nonequivalent microcanonical and canonical ensembles, the appearance of first-order phase transitions in the canonical ensemble, and thermodynamic metastable…

In the canonical formalism of statistical physics, a signature of a first order phase transition for finite systems is the bimodal distribution of an order parameter. Previous thermodynamical studies of nuclear sources produced in heavy-ion…

We study the global phase diagram of the infinite range Blume-Emery-Griffiths model both in the canonical and in the microcanonical ensembles. The canonical phase diagram is known to exhibit first order and continuous transition lines…

We compare phase transition(-like) phenomena in small model systems for both microcanonical and canonical ensembles. The model systems correspond to a few classical (non-quantum) point particles confined in a one-dimensional box and…

One-dimensional model of a system where first-order phase transition occurs is examined in the present paper. It is shown that basic properties of the phenomenon, such as a well defined temperature of transition, are caused both by…

We study phase transitions of small two dimensional Lennard Jones drops via microcanonical molecular dynamics in a broad energy range. We found that the caloric curve can be extended to high energies to comprehend high evaporation rates and…