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Griffiths singularities occurring in the unbinding of strongly disordered heteropolymers are studied. A model with two randomly distributed binding energies -1 and -v, is introduced and studied analytically by analyzing the Lee-Yang zeros…

We investigate the effects of disorder on a layered superconductor. The clean system is known to have a first order phase transition which is clearly identified by a sharp peak in the specific heat. The peak is lost abruptly as the strength…

First-order phase transitions are characterized by a discontinuous first derivative of the Gibbs free energy, so that volumes and entropies are discontinuous. Such transitions are common in the crystalline state, but extremely rare in…

This article reviews the unconventional effects of random disorder on magnetic quantum phase transitions, focusing on a number of new experimental and theoretical developments during the last three years. On the theory side, we address…

We study a model for the denaturation transition of DNA in which the molecules are considered as composed of a sequence of alternating bound segments and denaturated loops. We take into account the excluded-volume interactions between…

We consider disordered models of pinning of directed polymers on a defect line, including (1+1)-dimensional interface wetting models, disordered Poland--Scheraga models of DNA denaturation and other (1+d)-dimensional polymers in interaction…

In itinerant magnetic systems with disorder, the quantum Griffiths phase at T=0 is unstable to formation of a cluster glass (CG) of frozen droplet degrees of freedom. In the absence of the fluctuations associated with these degrees of…

In cold, dense quark matter, quarks of different flavor can form Cooper pairs which are anti-triplets under color and have total spin J=0. The transition to a phase where strange quarks condense with either up or down quarks is driven first…

We consider general disordered models of pinning of directed polymers on a defect line. This class contains in particular the $(1+1)$--dimensional interface wetting model, the disordered Poland--Scheraga model of DNA denaturation and other…

Experimental studies of the thermal denaturation of DNA yield a strong indication that the transition is first order. This transition has been theoretically studied since the early sixties, mostly within an approach in which the microscopic…

We give a short review of our recent works on the first-order quantum phase transitions in frustrated spin chains with orthogonal-dimer structure. When the ratio of the competing antiferromagnetic exchange couplings is varied, a first-order…

Using Brownian Dynamics, we study the dynamical behavior of a polymer grafted onto an adhesive surface close to the mechanically induced adsorption-stretching transition. Even though the transition is first order, (in the infinite chain…

The effect of quenched disorder on the low-energy properties of various antiferromagnetic spin ladder models is studied by a numerical strong disorder renormalization group method and by density matrix renormalization. For strong enough…

These lecture notes give a pedagogical introduction to phase transitions in disordered quantum systems and to the exotic Griffiths phases induced in their vicinity. We first review some fundamental concepts in the physics of phase…

We analyze the nucleation of supersolid order out of the superfluid ground state of bosons on the triangular lattice. While the stability of supersolidity against phase separation in this system is by now well established for…

Spherical confinement can act either stabilizing or destabilizing on the collapsed state of a semi-flexible polymer. General free-energy arguments suggest that the order of the unconstrained collapse transition is the distinguishing factor:…

A Dynamical Mean Field Theory analysis of the attractive Hubbard model is carried out. We focus on the normal state upon restricting to solutions where superconducting order is not allowed. Nevertheless a clear first-order pairing…

Disorder-broadened 1st order transitions may not carry the experimental signature of a latent heat. We discuss what experimental observation can provide a necessary and sufficient condition for characterizing this phase transition as 1st…

We investigate the low-energy properties of the orthogonal-dimer spin chain characterized by a frustrated dimer-plaquette structure. When the competing antiferromagnetic couplings are varied, the first-order quantum phase transition occurs…

The d-dimensional complex Ginzburg-Landau (GL) model is solved according to a variational method by separating phase and amplitude. The GL transition becomes first order for high superfluid density because of effects of phase fluctuations.…