A recent study linked the behavior of buying and selling in financial markets to the phenomenon of phase transitions that occur in physical systems with many interacting components. We urge caution with such findings. In particular, we show that the statistical technique employed in the study...

Influence of surrounding matter on the properties of clusters is considered by an approach combining the methods of statistical and quantum mechanics. A cluster is treated as a bound N-particle system and surrounding matter as thermostat. It is shown that, despite arbitrary strong interactions...

We generalize a wide class of time-continuous microscopic traffic models to include essential aspects of driver behaviour not captured by these models. Specifically, we consider (i) finite reaction times, (ii) estimation errors, (iii) looking several vehicles ahead (spatial anticipation), and...

In this paper, based on some mathematical results obtained by Yamabe, Osgood, Phillips and Sarnak, we demonstrate that in dimensions three and higher the famous Ginzburg–Landau equations used in the theory of phase transitions can be obtained (without any approximations) by minimization of the...

The introduction of a metric onto the space of parameters in models in statistical mechanics and beyond gives an alternative perspective on their phase structure. In such a geometrisation, the scalar curvature, R, plays a central role. A non-interacting model has a flat geometry (R=0), while R...

Equilibrium thermodynamical characteristics of ferrosmectics are estimated under conditions when both magnetic and steric interparticle interactions are taken into account. Deformation and condensation phase transitions in ferrosmectics are studied.

The phenomenon of partial equivalence of statistical ensembles is illustrated by discussing two examples, the mean-field XY and the mean-field spherical model. The configurational parts of these systems exhibit partial equivalence of the microcanonical and the canonical ensemble. Furthermore,...

We classify the matrix product states having only spin-flip and parity symmetries, which can be constructed from two dimensional auxiliary matrices. We show that there are three distinct classes of such states and in each case, we determine the parent Hamiltonian and the points of possible...

Ising or Potts models of ferromagnetism have been widely used to describe locally interacting social or economic systems. We consider a related model, introduced by Sznajd to describe the evolution of consensus in a society. In this model, the opinion or state of any spins can only be changed...

We discuss a simple model of correlated assets capturing the feedback effects induced by portfolio investment in the covariance dynamics. This model predicts an instability when the volume of investment exceeds a critical value. Close to the critical point the model exhibits dynamical...