arXiv subjects

F. Seno

Publications and source records attributed to F. Seno.

22 records · Page 2Linked to original sources

arXiv1995

Modulated structures stabilised by spin softening: an expansion in inverse spin anisotropy

We develop an analytic approach which allows us to study the behaviour of spin models with competing interactions and $p$-fold spin anisotropy, $D$, in the limit where the pinning potential which results from $D$ is large. This is an expansion in inverse spin anisotropy which must be carried out to all orders where necessary. Interesting behaviour occurs near where the boundary between different ground states is infinitely degenerate for infinite $D$. Here as $D$ decreases and the spins are allowed to soften, we are able to demonstrate the existence of several different behaviours ranging from a single first-order boundary to infinite series of commensurate phases. The method is illustrated by considering the soft chiral clock model and the soft clock model with first- and second-neighbour competing interactions. In the latter case the results are strongly dependent on the value of $p$.

cond-mat↗

arXiv1995

Optimal self-avoiding paths in dilute random medium

By a new type of finite size scaling analysis on the square lattice, and by renormalization group calculations on hierarchical lattices we investigate the effects of dilution on optimal undirected self-avoiding paths in a random environment. The behaviour of the optimal paths remains the same as for directed paths in undiluted medium, as long as forbidden bonds are not exceeding the percolation threshold. Thus, overhanging configurations do not alter the standard self-affine directed polymer scaling regime, even above the directed threshold, when they become unavoidable. When dilution reaches the undirected threshold, the optimal path becomes fractal, with fractal dimension equal to $D_{\rm min}$, the dimension of the minimal length path on percolation cluster backbone. In this regime the optimal path energy fluctuation, $\overline{ΔE}$, can be ascribed entirely to minimal length fluctuations, and satisfies $\overline{ΔE} \propto L^ω$, with $ω=1.02 \pm 0.06$ in $2d$, $L$ being the Euclidean distance. Hierarchical lattice calculations confirm that $ω$ is also the exponent of the leading scaling correction to $\overline E \propto L^{D_{\rm min}}$. Upon approaching threshold, the probability, ${\cal R}$, that the optimal path does not stick entirely on the minimal length one, obeys ${\cal R} \sim \left( Δp\right) ^ρ$, with $ρ\sim 1.0 \pm 0.05$ on hierarchical lattices. Such behaviour could be characteristic of the crossover to fractal regime. Transfer matrix results on square lattice show that a similar full sticking does not occur for directed paths at the directed percolation threshold.

cond-mat↗

arXiv1995

An Upsilon Point in a Spin Model

We present analytic evidence for the occurrence of an upsilon point, an infinite checkerboard structure of modulated phases, in the ground state of a spin model. The structure of the upsilon point is studied by calculating interface--interface interactions using an expansion in inverse spin anisotropy.

cond-mat↗

arXiv1994

Spin Softening in Models with Competing Interactions: A New High Anisotropy Expansion to All Orders

An expansion in inverse spin anisotropy, which enables us to study the behaviour of discrete spin models as the spins soften, is developed. In particular we focus on models, such as the chiral clock model and the $p$-state clock model with competing first and second neighbour interactions, where there are special multiphase points at zero temperature at which an infinite number of ground states are degenerate. The expansion allows calculation of the ground state phase diagram near these points as the spin anisotropy, which constrains the spin to take discrete values, is reduced from infinity. Several different behaviours are found, from a single first order phase boundary to infinite series of commensurate phases.

cond-mat↗