k-core percolation is a percolation model which gives a notion of network functionality and has many applications in network science. In analyzing the resilience of a network under random damage, an extension of this model is introduced, allowing different vertices to have their own degree of resilience. This extension is named heterogeneous k-core percolation and it is characterized by several...

Here we present a synopsis of related work [1, 2] describing a study of black hole threshold phenomena for a self-gravitating massive complex scalar field in spherical symmetry. Studies of models of gravitational collapse have revealed structure which can arise near the threshold of black hole formation. The solutions in this regime are known as " critical solutions," and their properties as " ...

Motivated by biological protocols that require transfer of large pieces of DNA into cells, we here review several aspects of osmotic swelling and lysis of semipermeable unilamellar vesicles. Swelling involves a continuous phase transition from a fluctuating flaccid state to a maximum volume turgid state, without a divergent correlation length and with exponents that violate the hyperscaling rel...

The supply and consumption of metabolites in living cells are catalyzed by enzymes. Here we consider two of the simplest schemes where one substrate is eliminated through Michaelis-Menten kinetics, and where two types of substrates are joined together by an enzyme. It is demonstrated how steady-state substrate concentrations can change ultrasensitively in response to changes in their supply rat...

Longitudinal (11 c) and transverse (LC) nonlinear susceptibilities have been measured on the Ising-type ZnMn spin glass. The critical exponents obtained from the scaling hypothesis depend on the anisotropy/exchange ratio, which can suggest a crossover effect from Heisenberg to Ising spin glasses in real RKKY systems. Critical behaviors of the nonlinear susceptibility in spin glasses have been e...

Synthetic non-conservative systems with parity-time (PT) symmetric gain-loss structures can exhibit unusual spontaneous symmetry breaking that accompanies spectral singularity. Recent studies on PT symmetry in optics and weakly interacting open quantum systems have revealed intriguing physical properties, yet many-body correlations still play no role. Here by extending the idea of PT symmetry t...

Using Monte Carlo methods and finite-size scaling, we investigate surface critical phenomena in the bond-percolation model on the simple-cubic lattice with two open surfaces in one direction. We decompose the whole lattice into percolation clusters and sample the surface and bulk dimensionless ratios Q1 and Qb, defined on the basis of the moments of the cluster-size distribution. These ratios a...

1. Introduction This paper has three parts. The first part is a simplified presentation of the basic ideas of the renormalization group and the ε expansion applied to critical phenomena , following roughly a summary exposition given in 1972 1. The second part is an account of the history (as I remember it) of work leading up to the papers in I971-1972 on the renormalization group. Finally, some...

1 Field Theory 2 1.1 Canonical Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Green’s Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Euclidean Time Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Example: Free Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 Functional Integral Formulation...