Related papers: Critical Behavior and Universality Classes for an …
The critical phase surface of a system, in general, can depend on one or more parameters. We show that by calculating the Gini index ($g$) of any suitably defined response function of a system, the critical phase surface can always be…
Quantum phase transition in the one-dimensional period-two and uniform quantum compass model are studied by using the pseudo-spin transformation method and the trace map method. The exact solutions are presented, the fidelity, the…
Let X_0=0, X_1, X_2, ..., be an aperiodic random walk generated by a sequence xi_1, xi_2, ..., of i.i.d. integer-valued random variables with common distribution p(.) having zero mean and finite variance. For an N-step trajectory…
The critical behaviour of systems belonging to the three-dimensional Ising universality class is studied theoretically using the collective variables (CV) method. The partition function of a one-component spin system is calculated by the…
We study the critical behavior at the ordinary surface universality class of the three-dimensional O($N$) model, bounded by a two-dimensional surface. Using high-precision Monte Carlo simulations of an improved lattice model, where the…
A general case of a spatially nonuniform planar layered Ising model, or an equivalent quantum Ising chain, is analysed with an exact functional real space renormalization group. Various surface, finite size, quasiperiodic and random layer…
Regularization is widely used in statistics and machine learning to prevent overfitting and gear solution towards prior information. In general, a regularized estimation problem minimizes the sum of a loss function and a penalty term. The…
We establish minimax optimal rates of convergence for estimation in a high dimensional additive model assuming that it is approximately sparse. Our results reveal an interesting phase transition behavior universal to this class of high…
Inferring the presence of critical dynamics from continuous measure- ments is a challenging problem. We solve this problem by showing that continuous narrowband dynamics from a critical system exhibit qualita- tively differing behaviors…
Universality, namely distributional invariance, is a well-known property for many random structures. For example, it is known to hold for a broad range of variational problems with random input. Much less is known about the algorithmic…
The two-dimensional $J$-$J^\prime$ dimerized quantum Heisenberg model is studied on the square lattice by means of (stochastic series expansion) quantum Monte Carlo simulations as a function of the coupling ratio \hbox{$\alpha=J^\prime/J$}.…
We study fidelity susceptibility in one-dimensional asymmetric Hubbard model, and show that the fidelity susceptibility can be used to identify the universality class of the quantum phase transitions in this model. The critical exponents…
We present a general framework for understanding and analyzing critical behaviour in gravitational collapse. We adopt the method of renormalization group, which has the following advantages. (1) It provides a natural explanation for various…
One of the most impressive features of continuous phase transitions is the concept of universality, that allows to group the great variety of different critical phenomena into a small number of universality classes. All systems belonging to…
We investigate the controversial issue of the existence of universality classes describing critical phenomena in three-dimensional statistical systems characterized by a matrix order parameter with symmetry O(2)xO(N) and symmetry-breaking…
We perform large-scale computer simulations of an off-lattice two-dimensional model of active particles undergoing a motility-induced phase separation (MIPS) to investigate the systems critical behaviour close to the critical point of the…
In this paper, we consider the problem of recovering a sparse signal based on penalized least squares formulations. We develop a novel algorithm of primal-dual active set type for a class of nonconvex sparsity-promoting penalties, including…
We propose a generalized Dicke model which supports a quantum tricritical point. We map out the phase diagram and investigate the critical behaviors of the model through exact low-energy effective Hamiltonian in the thermodynamic limit. As…
We describe a new universality class of dynamical quantum phase transitions of the Loschmidt amplitude of quantum spin chains off equilibrium criticality. We demonstrate that in many cases it is possible to change the conventional linear…
We describe a probabilistic, {\it sublinear} runtime, measurement-optimal system for model-based sparse recovery problems through dimensionality reducing, {\em dense} random matrices. Specifically, we obtain a linear sketch $u\in \R^M$ of a…