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This dissertation develops, for several families of statistical mechanical and random growth models, techniques for analyzing infinite-volume asymptotics. In the statistical mechanical setting, we focus on the low-temperature phases of spin…
To model discriminative, i.e. competition induced, self-thinning in even-aged forest stands a concept has been explored that discriminative mortality alters spatial arrangement of trees which in turn alters the mortality. Function of…
We investigate theoretically the transfer of excitation along a one dimensional chain of monomers for a situation in which initially the excitation is shared coherently by two monomers. We show that depending on the relative phase between…
We investigate the effect of correlated disorder on the localization transition undergone by a renewal sequence with loop exponent $\alpha$ > 0, when the correlated sequence is given by another independent renewal set with loop exponent…
A simple model of cyclically competing species on a directed graph with quenched disorder is proposed as an extension of the rock-paper-scissors model. By assuming that the effects of loops in a directed random graph can be ignored in the…
We consider the continuum directed random polymer (CDRP) model that arises as a scaling limit from $1+1$ dimensional directed polymers in the intermediate disorder regime. We show that for a point-to-point polymer of length $t$ and any…
This paper focuses on directed polymers pinned at a disordered and correlated interface. We assume that the disorder sequence is a q-order moving average and show that the critical curve of the annealed model can be expressed in terms of…
In this article we study a \emph{non-directed} polymer model in dimension $d\ge 2$: we consider a simple symmetric random walk on $\mathbb{Z}^d$ which interacts with a random environment, represented by i.i.d. random variables…
Semiflexible polymers in poor solvents exhibit a rich variety of collapsed morphologies, including globules, toroids, and rodlike bundles, arising from the competition between attractive interactions and chain stiffness. Computer…
A physics-based analytical model describing the phase transition from crystalline to conformationally disordered (condis) crystalline phase is developed. In the model, the free energy is written as a function of temperature and the lattice…
We study the pinning transition in a (1+1)-dimensional lattice model of a fluctuating interface interacting with a corrugated impenetrable wall. The interface is modeled as an $N$-step directed one-dimensional random walk on the half-line…
We consider a polymer with configuration modeled by the path of a Markov chain, interacting with a potential $u+V_n$ which the chain encounters when it visits a special state 0 at time $n$. The disorder $(V_n)$ is a fixed realization of an…
The presence of frozen-in or quenched disorder in a system can often modify the nature of its phase transition. A particular instance of this phenomenon is the so-called rounding effect: it has been shown in many cases that the free-energy…
One of the major factors governing the mode of failure in disordered solids is the effective range $R$, over which the stress field is modified following a local rupture event. In random fiber bundle model, considered as a prototype of…
Critical properties of quantum spin chains with varying degrees of disorder are studied at zero temperature by analytical and extensive density matrix renormalization methods. Generally the phase diagram is found to contain three phases.…
After a general introduction to the field, we describe some recent results concerning disorder effects on both `random walk models', where the random walk is a dynamical process generated by local transition rules, and on `polymer models',…
We present a detailed, quantitative study of the competition between interaction- and disorder-induced effects in electronic systems. For this the Anderson-Hubbard model with diagonal disorder is investigated analytically and by Quantum…
The phase diagram of the collapse of a two-dimensional infinite branched polymer interacting with the solvent and with itself through contact interactions is studied from the $q\to 1$ limit of an extension of the $q-$ states Potts model.…
We consider spin systems between a finite number $N$ of "species" or "phases" partitioning a cubic lattice $\mathbb{Z}^d$. We suppose that interactions between points of the same phase are coercive, while between point of different phases…
We construct a phenomenological theory of self-localization of directed polymers in d+1 dimensions. In d=1 we show that the polymer is always self-localized, whereas in d=2 there is a phase transition between localized and free states. We…