Using molecular dynamics with an accurate many-body potential, we studied the rapid expansion of Ta metal following the high compression ~50 to 100 GPa! induced by high velocity (2 to 4 km/s! impact. We find that catastrophic failure in this system coincides with a critical behavior characterized by a void distribution of the form N(v)}V, with t;2.2. This corresponds to a threshold in which per...

An introduction to the theory of critical behavior at Lifshitz points is given, and the recent progress made in applying the field-theoretic renormalization group (RG) approach to φ nvector models representing universality classes of m-axial Lifshitz points is surveyed. The origins of the difficulties that had hindered a full two-loop RG analysis near the upper critical dimension for more than ...

The effect of quenched impurities on systems which undergo first-order phase transitions is studied within the framework of the q-state Potts model. For large q a mapping to the random field Ising model is introduced which provides a simple physical explanation of the absence of any latent heat in 2D, and suggests that in higher dimensions such systems should exhibit a tricritical point with a ...

The classical, thermally driven transition in the dipolar-coupled Ising ferromagnet LiHoF 4 sTc ­ 1.53 Kd can be converted into a quantum transition driven by a transverse magnetic field Ht at T ­ 0. The transverse field, applied perpendicular to the Ising axis, introduces channels for quantum relaxation, thereby depressing Tc . We have determined the phase diagram in the Ht-T plane via magneti...

We study the critical behavior of the random q-state Potts quantum chain by density-matrix renormalization techniques. Critical exponents are calculated by scaling analysis of finite lattice data of short chains (L<16) averaging over all possible realizations of disorder configurations chosen according to a binary distribution. Our numerical results show that the critical properties of the mode...

We present two classes of nonequilibrium models with critical behavior. Each model is characterized by an integer q > 1, and is defined on configurations of q-valued spins on regular lattices. The definitions of the models are very similar to the updating rules in Wolff’s algorithm for the Potts model, but both classes break detailed balance, except for q = 2 and q = ∞. In the first case both m...

In the simple mean-field SIS and SIR epidemic models, infection is transmitted from infectious to susceptible members of a finite population by independent p−coin tosses. Spatial variants of these models are proposed, in which finite populations of size N are situated at the sites of a lattice and infectious contacts are limited to individuals at neighboring sites. Scaling laws for these models...

Critical behavior was studied with a crosslinking system obtained by living anionic polymerization, where the primary chain length was kept constant and the crosslinking density was varied. Gelation was found at a critical ratio of crosslinker

The large-N saddle-point equations for the principal chiral models defined on a d − 1 dimensional simplex are derived from the external field problem for unitary integrals. The saddle point equation are studied analytically and numerically in many relevant instances, including d = 4 and d → ∞, with special attention to the critical domain, which is found to correspond to βc = 1/d for all d. Rel...

This article briefly reviews three topics related to the quantum critical behavior of certain heavy-fermion systems. First, we summarize an extended dynamical mean-field theory for the Kondo lattice, which treats on an equal footing the quantum fluctuations associated with the Kondo and RKKY couplings. The resulting dynamical mean-field equations describe a Kondo impurity model with an addition...