Related papers: Extracting critical exponents for sequences of num…
We present a novel algorithm that allows one to obtain temperature dependent properties of quantum lattice models in the thermodynamic limit from exact diagonalization of small clusters. Our Numerical Linked Cluster (NLC) approach provides…
In general, perturbative expansions of observables in powers of the coupling constant in quantum field theories are asymptotic series. In many cases it is possible to apply resummation techniques to assign a unique finite value to an…
We present simulation results for the contact process on regular, cubic networks that are composed of a one-dimensional lattice and a set of long edges with unbounded length. Networks with different sets of long edges are considered, that…
We investigate the quantum-critical behavior between the rung-singlet phase with hidden string order and the N\'eel phase with broken $SU(2)$-symmetry on quantum spin ladders with algebraically decaying unfrustrated long-range Heisenberg…
Scanning probes reveal complex, inhomogeneous patterns on the surface of many condensed matter systems. In some cases, the patterns form self-similar, fractal geometric clusters. In this paper, we advance the theory of criticality as it…
These lecture notes introduce quantum spin systems and several computational methods for studying their ground-state and finite-temperature properties. Symmetry-breaking and critical phenomena are first discussed in the simpler setting of…
We study the mutual information between two lattice-blocks in terms of von Neumann entropies for one-dimensional infinite lattice systems. Quantum $q$-state Potts model and transverse field spin-$1/2$ XY model are considered numerically by…
This paper presents a generalized technology of extraction of explicit knowledge from data. The main ideas are 1) maximal reduction of network complexity (not only removal of neurons or synapses, but removal all the unnecessary elements and…
A quantitative first-principles description of complex substitutional materials like alloys is challenging due to the vast number of configurations and the high computational cost of solving the quantum-mechanical problem. Therefore,…
We investigate the short time quantum critical dynamics in the imaginary time relaxation processes of finite size systems. Universal scaling behaviors exist in the imaginary time evolution and in particular, the system undergoes a critical…
We use series expansions to study dynamics of equilibrium and non-equilibrium systems on networks. This analytical method enables us to include detailed non-universal effects of the network structure. We show that even low order…
We consider a special case of the n-component cubic model on the square lattice, for which an expansion exists in Ising-like graphs. We construct a transfer matrix and perform a finite-size-scaling analysis to determine the critical points…
In two different phase transition models of nuclear fragmentation we show that the emission of pre-equilibrium particles and mixing of events from different classes cannot be ignored in the analysis of nuclear fragmentation data in terms of…
Nonsingular estimation of high dimensional covariance matrices is an important step in many statistical procedures like classification, clustering, variable selection an future extraction. After a review of the essential background…
We compute the critical exponents for nonextensive $\lambda\phi^{3}$ scalar field theory for all loop orders and $|q - 1| < 1$. We apply the results for both nonextensive percolation and Lee-Yang edge singularity problems. The corresponding…
I use the two-step density-matrix renormalization group method to extract the critical exponents $\beta$ and $\nu$ in the transition from a N\'eel $Q=(\pi,\pi)$ phase to a magnetically disordered phase with a spin gap. I find that the…
We present a novel extrapolation scheme for high order series expansions. The idea is to express the series, obtained in orders of an external variable, in terms of an internal parameter of the system. Here we apply this method to the…
Given the first 20-100 coefficients of a typical generating function of the type that arises in many problems of statistical mechanics or enumerative combinatorics, we show that the method of differential approximants performs surprisingly…
Exponential time differencing methods is a power tool for high-performance numerical simulation of computationally challenging problems in condensed matter physics, fluid dynamics, chemical and biological physics, where mathematical models…
We investigate a method for extracting nonlinear principal components (NPCs). These NPCs maximize variation subject to smoothness and orthogonality constraints; but we allow for a general class of constraints and multivariate probability…