相关论文: The escape transition in a self-avoiding walk mode…

We present the exact solutions of various directed walk models of polymers confined to a slit and interacting with the walls of the slit via an attractive potential. We consider three geometric constraints on the ends of the polymer and…

In a recent letter, a simple method was proposed to generate solvable models that predict the critical properties of statistical systems in hyperspherical geometries. To that end, it was shown how to reduce a random walk in $D$ dimensions…

We study a class of quantum phase transitions between featureless bosonic atomic insulators in $(2+1)$ dimensions, where each phase exhibits neither topological order nor protected edge modes. Despite their lack of topology, these…

It is shown that the effective string recently introduced to describe the long distance dynamics of 3D gauge systems in the confining phase has an intriguing description in terms of models of 2D self-avoiding walks in the dense phase. The…

Self-avoiding walks self-interacting via nearest neighbours (ISAW) and self-avoiding trails interacting via multiply-visited sites (ISAT) are two models of the polymer collapse transition of a polymer in dilute solution. On the square…

We consider the model of self-avoiding walks on the $d$-dimensional hypercubic lattice interacting with a $d^*$-dimensional defect, where $1\leq d^*<d$. Such an interaction can be attractive or repulsive, and is controlled by a Boltzmann…

An infinite hierarchy of layering transitions exists for model polymers in solution under poor solvent or low temperatures and near an attractive surface. A flat histogram stochastic growth algorithm known as FlatPERM has been used on a…

Modeling of polymer chains has received a lot of attention in mathematics. In fact, probabilistic models that naturally arise in statistical mechanics have been widely studied by mathematicians for the very challenging and novel problems…

We consider various lattice models of polymers: lattice trees, lattice animals, and self-avoiding walks. The polymer interacts with a surface (hyperplane), receiving a unit energy reward for each site in the surface. There is an adsorption…

Topological gapless phases of matter have been a recent interest among theoretical and experimental condensed matter physicists. Fermionic chains with extended nearest neighbor couplings have been observed to show unique topological…

We investigate random walks on a lattice with imperfect traps. In one dimension, we perturbatively compute the survival probability by reducing the problem to a particle diffusing on a closed ring containing just one single trap. Numerical…

An exact calculation of the phase diagram for a loop gas model on the brickwork lattice is presented. The model includes a bending energy. In the dense limit, where all the lattice sites are occupied, a phase transition occuring at an…

We write exact equations for the thermodynamic properties of a linear polymer molecule confined to walk on a lattice of finite size. The dimension of the space in which the lattice resides can be arbitrary. We also calculate polymer…

Phase transitions are a central theme of statistical mechanics, and of probability more generally. Lattice spin models represent a general paradigm for phase transitions in finite dimensions, describing ferromagnets and even some fluids…

We consider a simple cubic lattice self-avoiding walk model of 3-star polymers adsorbed at a surface and then desorbed by pulling with an externally applied force. We determine rigorously the free energy of the model in terms of properties…

We study biased random walkers on lattices with randomly dispersed static traps in one, two and three dimensions. As the external bias is increased from zero the system undergoes a phase transition, most clearly manifested in the asymptotic…

We describe method to discuss thermodynamics of a defected semi-flexible homo-polymer chain in the two and three dimensions using fully directed self-avoiding walk lattice model. The defects are located along a line and these defects are…

Stretched polymers with attractive interaction are studied in two and three dimensions. They are described by biased self-avoiding random walks with nearest neighbour attraction. The bias corresponds to opposite forces applied to the first…

We consider a model of semi-flexible interacting self-avoiding trails (sISAT's) on a lattice, where the walks are constrained to visit each lattice edge at most once. Such models have been studied as an alternative to the self-attracting…

Single three dimensional polymers confined to a slab, i.e. to the region between two parallel plane walls, are studied by Monte Carlo simulations. They are described by $N$-step walks on a simple cubic lattice confined to the region $1 \le…