arXiv subjects

Kari Eloranta

Publications and source records attributed to Kari Eloranta.

6 recordsLinked to original sources

arXiv2018

The bounded 15-vertex model

The 15-vertex model of Statistical Mechanics is studied on a square domain with partially oriented boundary. With DWBC the model would reduce to the six-vertex model, but more general boundary configurations are available. After establishing the dynamic version of the model we simulate with it to find the typical equilibrium states for a set of increasingly complex boundaries. Among others they yield almost isotropic non-trivial limit shapes even though the microscopic model is highly asymmetric.

cond-mat.stat-mech↗

arXiv2017

The bounded 19-vertex model

We study the 19-vertex model of Statistical Mechanics in a square with the domain wall boundary condition. Using the minimal set of generating flip actions we build a parametrized dynamic version of the model. For all observed dynamic weight values the equilibrium states exhibit clear limit shapes. Although the model in a way incorporates the 6-vertex model, the reason for the existence of the limit shape is fundamentally more general. We conclude with a further study relating the local path geometry to the macroscopic shape geometry.

cond-mat.stat-mech↗

arXiv2013

Sequences with long range exclusions

Given an alphabet $S$, we consider the size of the subsets of the full sequence space $S^{\rm {\bf Z}}$ determined by the additional restriction that $x_i\not=x_{i+f(n)},\ i\in {\rm {\bf Z}},\ n\in {\rm {\bf N}}.$ Here $f$ is a positive, strictly increasing function. We review an other, graph theoretic, formulation and then the known results covering various combinations of $f$ and the alphabet size. In the second part of the paper we turn to the fine structure of the allowed sequences in the particular case where $f$ is a suitable polynomial. The generation of sequences leads naturally to consider the problem of their maximal length, which turns out highly random asymptotically in the alphabet size.

math.PR↗

arXiv2009

Hard Core entropy: lower bounds

We establish lower bounds for the entropy of the Hard Core Model on a few 2d lattices $\scriptstyle {\rm {\bf L}}.$ In this model the allowed configurations inside $\scriptstyle \{0,1\}^{\rm {\bf L}}$ are the one's in which the nearest neighbor $\scriptstyle 1$'s are forbidden. Our method which is based on a sequential fill-in scheme is unbiassed and thereby yields in principle arbitrarily good estimates for the topological entropy. The procedure also gives some detailed information on the support of the measure of maximal entropy.

math.PR↗

arXiv2009

Archimedean Ice

The striking boundary dependency (the Arctic Circle phenomenon) exhibited in the ice model on the square lattice extends to other planar set-ups. We present these findings for the triangular and the Kagome lattices. Critical connectivity results guarantee that ice configurations can be generated using the simplest and most efficient local actions. Height functions are utilized throughout the analysis. At the end there is a surprise in store: on the remaining Archimedean lattice for which the ice model can be defined, the 3.4.6.4. lattice, the long range behavior is completely different from the other cases.

math-ph↗

arXiv2009

Dense packing on uniform lattices

We study the Hard Core Model on the graphs ${\rm {\bf \scriptstyle G}}$ obtained from Archimedean tilings i.e. configurations in $\scriptstyle \{0,1\}^{\rm {\bf G}}$ with the nearest neighbor 1's forbidden. Our particular aim in choosing these graphs is to obtain insight to the geometry of the densest packings in a uniform discrete set-up. We establish density bounds, optimal configurations reaching them in all cases, and introduce a probabilistic cellular automaton that generates the legal configurations. Its rule involves a parameter which can be naturally characterized as packing pressure. It can have a critical value but from packing point of view just as interesting are the noncritical cases. These phenomena are related to the exponential size of the set of densest packings and more specifically whether these packings are maximally symmetric, simple laminated or essentially random packings.

math-ph↗