Related papers: Remarks about the Phase Transitions within the Mic…
This paper presents an in-depth analysis of the anatomy of both thermodynamics and statistical mechanics, together with the relationships between their constituent parts. Based on this analysis, using the renormalization group and…
Topological quantum phase transitions are characterised by changes in global topological invariants. These invariants classify many body systems beyond the conventional paradigm of local order parameters describing spontaneous symmetry…
A local criterion of topological phase transitions is established based on the Morse theory: a topological phase transition occurs when the count of Morse critical points of the order function changes. The locations in space where this…
Equilibrium statistics of Hamiltonian systems is correctly described by the microcanonical ensemble. Classically this is the manifold of all points in the $N-$body phase space with the given total energy. Due to Boltzmann's principle,…
Topological properties of a periodic condensed matter system are global features of its Brillouin zone (BZ). In contrast, the validity of effective low energy theories is usually limited to the vicinity of a high symmetry point in the BZ.…
It is commonly assumed that topological phase transitions in topological superconductors are accompanied by a closing of the topological gap or a change of the symmetry of the system. We demonstrate that an unconventional topological phase…
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…
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 discuss general thermodynamic properties of molecular structure formation processes like protein folding by means of simplified, coarse-grained models. The conformational transitions accompanying these processes exhibit similarities to…
Topological phase transitions in band models are usually associated to the gap closing between the highest valance band and the lowest conduction band, which can give rise to different types of nodal structures, such as Dirac/Weyl points,…
A characteristic feature of topological systems is the presence of robust gapless edge states. In this work the effect of time-dependent perturbations on the edge states is considered. Specifically we consider perturbations that can be…
In the realm of statistical mechanics, it has been established that there is no distinction between the micro-canonical and canonical ensembles in the thermodynamic limit. However, this paradigm may alter when addressing statistical…
Continuous phase transitions can be classified into ones characterized by local-order parameters and others that need additional topological constraints. The critical dynamics near the former transitions have been extensively studied, but…
The topological hypothesis claims that phase transitions in a classical statistical mechanical system are related to changes in the topology of the level sets of the Hamiltonian. So far, the study of this hypothesis has been restricted to…
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…
We present a dimensional reduction argument to derive the classification reduction of fermionic symmetry protected topological phases in the presence of interactions. The dimensional reduction proceeds by relating the topological character…
Two examples of Microcanonical Potts models, 2-dimensional nearest neighbor and mean field, are considered via exact enumeration of states and analytical asymptotic methods. In the interval of energies corresponding to a first order phase…
Inverse phase transitions are striking phenomena in which an apparently more ordered state disorders under cooling. This behavior can naturally emerge in tricritical systems on heterogeneous networks and it is strongly enhanced by the…
The Hamiltonian dynamics associated to classical, planar, Heisenberg XY models is investigated for two- and three-dimensional lattices. Besides the conventional signatures of phase transitions, here obtained through time averages of…
For relaxor-ferroelectrics and relaxor-ferromagnets, Ehrenfest classification of phase transitions based on the discontinuity of entropy or specific heat etc. with temperature (T) gives no transition that contradicts the measured order…