We elaborate Weiermann-style phase transitions for Gordeev well-quasi-ordering (called well-partial-ordering below, abbr.: wpo) results with respect to nested finite sequences and nested finite trees under the homeomorphic embedding with symmetrical gap condition. For every nested partial ordering in question, E, we fix a natural extension of Peano Arithmetic, T, that proves the corresponding 2...

Structural phase transitions can be studied by a variety of techniques; macroscopic fields, X-ray, light and neutron diffraction, and resonance methods. The information which can be obtained by these different techniques about the order parameter and susceptibility at structural phase transitions is described and compared. Landau theory coupled with the 'sot~ mode' concept provides a simple pic...

It is generally believed that several phase transitions have taken place in the early Universe. The effects of cosmological phase transitions may well have been crucial for the evolution of the Universe, and thus for the existence of life as we know it. The cosmological phase transitions investigated here are related to strong and electroweak interactions. When the Universe was about 10 seconds...

We apply the theory of markov random fields on trees to derive a phase transition in the number of samples needed in order to reconstruct phylogenies. We consider the Cavender-Farris-Neyman model of evolution on trees, where all the inner nodes have degree at least 3, and the net transition on each edge is bounded by ǫ. Motivated by a conjecture by M. Steel, we show that if 2(1 − 2ǫ)2 > 1, then...

The geometrical approach to phase transitions is illustrated by simulating the hightemperature representation of the Ising model on a square lattice.

We start with the spinfluid: a nearly-homogeneous, 8-spinor medium, with small local spin(4,C) eddies and twists. As it expends, these seed a raft of intersecting codimension J singularities: a spinfoam, Σ. As Σ expands, the energy trapped in each (4 − J) brane varies as γ , where γ(t) ≡ a(t) a# is the scale factor. Summing on J = (0, 1, 2, 3, 4) creates a quartic dilation potential V (nJ ; γ) ...

These lecture notes give a basic introduction to the physics of phase transitions under non-equilibrium conditions. The notes start with a general introduction to non-equilibrium statistical mechanics followed by four parts. The first one discusses the universality class of directed percolation, which plays a similar role as the Ising model in equilibrium statistical physics. The second one giv...

The most spectacular consequence of interactions among particles is the appearance of new phases of matter whose collective behavior bears little resemblance to that of a few particles. How do the particles then transform from one macroscopic state to a completely different one. From a formal perspective, all macroscopic properties can be deduced from the free energy or the partition function. ...

summing the Boltzmann factor over all spin configurations {si}. The enumeration of all configurations cannot be done for d ≥ 3, and although possible in d = 2 is extremely hard there as well (a problem solved by Onsager). We will use an approximate solution technique known as mean field theory. Last term we solved the problem of noninteracting spins in a magnetic field described by the Hamilton...