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We study an ensemble of branched polymers which are embedded on other branched polymers. This is a toy model which allows us to study explicitly the reaction of a statistical system on an underlying geometrical structure, a problem of…
We analyze a one-dimensional spin-string model, in which string oscillators are linearly coupled to their two nearest neighbors and to Ising spins representing internal degrees of freedom. String-spin coupling induces a long-range…
We study grand--canonical and canonical properties of the model of branched polymers proposed in \cite{adfo}. We show that the model has a fourth order phase transition and calculate critical exponents. At the transition the exponent…
In recent times some interesting field theoretical descriptions of the statistical mechanics of entangling polymers have been proposed by various authors. In these approaches, a single test polymer fluctuating in a background of static…
A modified phase field crystal model in which the free energy may be minimised by an order parameter profile having isolated bumps is investigated. The phase diagram is calculated in one and two dimensions and we locate the regions where…
A system of two self and mutual interacting ring polymers, close together in space, can display several competing equilibrium phases and phase transitions. Using Monte Carlo simulations and combinatorial arguments on a corresponding lattice…
Recently it has been shown that a two-dimensional model of self-attracting polymers based on attracting segments displays two phase transitions, a theta-like collapse between swollen polymers and a globular state and another between the…
A statistical study of crumpled paper is allowed by a minimal 1D model: a self-avoiding line bent at sharp angles -- in which resides the elastic energy -- put in a confining potential. Many independent equilibrium configurations 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…
The recently introduced nested sampling algorithm allows the direct and efficient calculation of the partition function of atomistic systems. We demonstrate its applicability to condensed phase systems with periodic boundary conditions by…
We study the bipartite entanglement per bond to determine characteristic features of the phase diagram of various quantum spin models in different spatial dimensions. The bipartite entanglement is obtained from a tensor network…
We show that a Calogero-Sutherland type model with anharmonic interactions of fourth and sixth orders leads to the matrix model corresponding to the branched polymers. We also show that by suitably modifying this model one can also obtain…
We propose a spectroscopic method of identifying broken symmetry states of bilayer graphene. We demonstrate theoretically that, in contrast to gapped states, a strained bilayer crystal or nematic phase of the electronic liquid are…
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 study surface plasmons in minimally-twisted gapped bilayer graphene that contains a triangular network of partial dislocations (or AB-BA domain walls) hosting topologically protected one-dimensional electronic states. We show that this…
We consider here a blend made of two types of polymers, $A$ and $B$, of different chemical nature. At high temperature the homogeneous mixture is cross-linked. As the temperature is lowered, the two species try to segregate but are kept…
We study a stochastic lattice gas of particles in one dimension with strictly finite-range interactions that respect the fracton-like conservation laws of total charge and dipole moment. As the charge density is varied, the connectivity of…
We analyze the crystallization and collapse transition of a simple model for flexible polymer chains on simple cubic and face-centered cubic lattices by means of sophisticated chain-growth methods. In contrast to bond-fluctuation polymer…
We explore the coupling between the helix-coil and coil-globule transitions of a helical polymer using Monte Carlo simulations. A very rich state diagram is found. Each state is characterized by a specific configuration of the chain which…
We solve a class of branched polymer models coupled to spin systems and show that they have no phase transition and are either always magnetized or never magnetized depending on the branching weights. By comparing these results with…