arXiv subjects

Milos Zahradnik

Publications and source records attributed to Milos Zahradnik.

3 recordsLinked to original sources

arXiv2005

Entropy-driven phase transition in a polydisperse hard-rods lattice system

We study a system of rods on the 2d square lattice, with hard-core exclusion. Each rod has a length between 2 and N. We show that, when N is sufficiently large, and for suitable fugacity, there are several distinct Gibbs states, with orientational long-range order. This is in sharp contrast with the case N=2 (the monomer-dimer model), for which Heilmann and Lieb proved absence of phase transition at any fugacity. This is the first example of a pure hard-core system with phases displaying orientational order, but not translational order; this is a fundamental characteristic feature of liquid crystals.

math.PR↗

arXiv1997

Non-periodic long-range order for fast decaying interactions at positive temperatures

We present the first example of an exponentially decaying interaction which gives rise to non-periodic long-range order at positive temperatures.

cond-mat.stat-mech↗

arXiv1996

The low-temperature phase of Kac-Ising models

We analyse the low temperature phase of ferromagnetic Kac-Ising models in dimensions $d\geq 2$. We show that if the range of interactions is $\g^{-1}$, then two disjoint translation invariant Gibbs states exist, if the inverse temperature $\b$ satisfies $\b -1\geq \g^\k$ where $\k=\frac {d(1-\e)}{(2d+1)(d+1)}$, for any $\e>0$. The prove involves the blocking procedure usual for Kac models and also a contour representation for the resulting long-range (almost) continuous spin system which is suitable for the use of a variant of the Peierls argument.

cond-mat↗