Related papers: Criticality Beyond Nonanalyticity: Intrinsic Micro…
Collective critical behavior is often identified with thermodynamic nonanalyticities and divergences emerging only in the infinite-size limit. Here we adopt a complementary viewpoint: criticality is a structural property due to the…
In contrast to the canonical ensemble where thermodynamic functions are smooth for all finite system sizes, the microcanonical entropy can show nonanalytic points also for finite systems, even if the Hamiltonian is smooth. The relation…
Nonanalyticities of thermodynamic functions are studied by adopting an approach based on stationary points of the potential energy. For finite systems, each stationary point is found to cause a nonanalyticity in the microcanonical entropy,…
We introduce a systematic classification method for the analogs of phase transitions in finite systems. This completely general analysis, which is applicable to any physical system and extends towards the thermodynamic limit, is based on…
The basic quantity for the description of the statistical properties of physical systems is the density of states or equivalently the microcanonical entropy. Macroscopic quantities of a system in equilibrium can be computed directly from…
In contrast to the canonical case, microcanonical thermodynamic functions can show nonanalyticities also for finite systems. In this paper we contribute to the understanding of these nonanalyticities by working out the relation between…
In statistical physics, phase transitions are arguably among the most extensively studied phenomena. In the computational approach to this field, the development of algorithms capable of estimating entropy across the entire energy spectrum…
It is discussed how phase transitions of first order (with phase separation and surface tension), continuous transitions and (multi)-critical points can be defined and classified for finite systems from the topology of the energy surface…
By means of the principle of minimal sensitivity we generalize the microcanonical inflection-point analysis method by probing derivatives of the microcanonical entropy for signals of transitions in complex systems. A strategy of…
On the phase diagram of a system undergoing a continuous phase transition of the second order, three lines, hyper-surfaces, convergent into the critical point feature prominently: the ordered and disordered phases in the thermodynamic…
Critical phase transitions contain a variety of deep and universal physics, and are intimately tied to thermodynamic quantities through scaling relations. Yet, these notions are challenged in the context of non-Hermiticity, where spatial or…
Superconducting diodes promise dissipation-less rectification, yet intrinsic platforms invariably have very low efficiencies. We reveal a fundamental thermodynamic origin of this behavior that is independent of microscopic details. Denoting…
Abrupt shifts in ecosystems, brains, markets, and climate are often diagnosed as signs of approaching a tipping point, i.e. a critical bifurcation where stability is lost. Here we reveal a broader and more deceptive mechanism:…
While classical theory of phase transitions deals with systems where shape variation is energetically neutral, the account of rigidity can lead to the emergence of new thermodynamic features. One of them is a special type of critical points…
The relation between saddle points of the potential of a classical many-particle system and the analyticity properties of its Boltzmann entropy is studied. For finite systems, each saddle point is found to cause a nonanalyticity in the…
Traditionally, phase transitions are defined in the thermodynamic limit only. We discuss how phase transitions of first order (with phase separation and surface tension), continuous transitions and (multi)-critical points can be seen and…
Microcanonical statistics can be well applied to non-extensive systems like nuclei, atomic clusters and systems at phase transitions of first order with inhomogeneous configurations like phase separation. No thermodynamic limit has to be…
A prototypical model of symmetry-broken active matter -- biased quorum-sensing active particles (bQSAPs) -- is used to extend notions of dynamic critical phenomena to the paradigmatic setting of driven transport, where characteristic…
We employ the microcanonical inflection-point analysis method, developed for the systematic identification and classification of phase transitions in systems of any size, to study the two-dimensional Ising model at various lattice sizes and…
Behavior of the Grand thermodynamic potential along with its derivatives, entropy and specific heat, is considered within a two-band model of an unconventional $s_\pm$ superconductor with nonmagnetic impurities. The transition $s_\pm \to…