相关论文: Critical Behavior and Universality Classes for an …

We discuss the order parameter correlation function in the vicinity of continuous phase transitions using a two-parameter scaling form G(k) = k_c^{-2} g(k\xi,k/k_c), where k is the wave-vector, \xi is the correlation length, and the…

In this work we have studied the QCD phase structure and critical dynamics related to the 3-$d$ $O(4)$ and $Z(2)$ symmetry universality classes in the two-flavor quark-meson low energy effective theory within the functional renormalization…

Detection of phase transitions is a critical task in statistical physics, traditionally pursued through analytic methods and direct numerical simulations. Recently, machine-learning techniques have emerged as promising tools in this…

We present a field theoretic renormalization group study for the critical behaviour of a uniformly driven diffusive system with quenched disorder, which is modelled by different kinds of potential barriers between sites. Due to their…

We derive a new renormalization group to calculate a non-trivial critical exponent of the divergent correlation length which gives a universality classification of essential singularities in infinite-order phase transitions. This method…

We consider the problem of high-dimensional misspecified phase retrieval. This is where we have an $s$-sparse signal vector $\mathbf{x}_*$ in $\mathbb{R}^n$, which we wish to recover using sampling vectors…

Our model is a generalized linear programming relaxation of a much studied random K-SAT problem. Specifically, a set of linear constraints C on K variables is fixed. From a pool of n variables, K variables are chosen uniformly at random and…

Recently, the number of non-standard percolation models has proliferated. In all these models, there exists a phase transition at which long range connectivity is established, if local connectedness increases through a threshold $p_c$. In…

Second-order phase transitions are characterised by critical scaling and universality. The singular behaviour of thermodynamic quantities at the transition, in particular, is determined by critical exponents of the universality class of the…

We study slow variation (both spatial as well as temporal) of a parameter of a system in the vicinity of discontinuous quantum phase transitions, in particular, a discontinuity critical point (DCP) (or a first-order critical point). We…

In long-range percolation on $\mathbb{Z}^d$, points $x$ and $y$ are connected by an edge with probability $1-\exp(-\beta\|x-y\|^{-d-\alpha})$, where $\alpha>0$ is fixed and $\beta \geq 0$ is a parameter. As $d$ and $\alpha$ vary, the model…

Matrix product states, a key ingredient of numerical algorithms widely employed in the simulation of quantum spin chains, provide an intriguing tool for quantum phase transition engineering. At critical values of the control parameters on…

We study the imaginary-time relaxation critical dynamics of a quantum system with a vanishing initial correlation length and an arbitrary initial order parameter $M_0$. We find that in quantum critical dynamics, the behavior of $M_0$ under…

The scaling behaviour of euclidean quantum gravity at an asymptotically safe critical point is studied by means of the exact renormalisation group. Gauge independence is ensured via a specific parameterisation of metric fluctuations…

Universality, encompassing critical exponents, scaling functions, and dimensionless quantities, is fundamental to phase transition theory. In finite systems, universal behaviors are also expected to emerge at the pseudocritical point.…

We analyze critical points that can be induced in glassy systems by the presence of constraints. These critical points are predicted by the Mean Field Thermodynamic approach and they are precursors of the standard glass transition in…

We address the problem of variable selection in a high-dimensional but sparse mean model, under the additional constraint that only privatised data are available for inference. The original data are vectors with independent entries having a…

We consider the estimation of the transition matrix in the high-dimensional time-varying vector autoregression (TV-VAR) models. Our model builds on a general class of locally stationary VAR processes that evolve smoothly in time. We propose…

It is well known that the similar universal behavior of infinite-size (bulk) systems of different nature requires the same basic conditions: space dimensionality; number components of order parameter; the type (short- or long-range) of the…

Many modern data analysis algorithms either assume or are considerably more efficient if the distances between the data points satisfy a metric. These algorithms include metric learning, clustering, and dimension reduction. As real data…