Related papers: Pad\'e Approximation and Partition Function Zeros
There are numerous methods to characterize topology and its boundary zero modes, yet their statistical mechanical properties have not received as much attention as other approaches. Here, we investigate the Fisher zeros and thermofield…
Pad'e approximants are used to improve the convergence behavior of perturbative results in massless scalar and gauge field theories at finite temperature.
Quantum phase transitions are a fascinating area of condensed matter physics. The extension through complexification not only broadens the scope of this field but also offers a new framework for understanding criticality and its statistical…
The study of zeros of partition functions, initiated by Yang and Lee, provides an important qualitative and quantitative tool in the study of critical phenomena. This has frequently been used for periodic as well as hierarchical lattices.…
Elliptic Partial Differential Equations (PDEs) play a central role in computing the equilibrium conditions of physical problems (heat, gravitation, electrostatics, etc.). Efficient solutions to elliptic PDEs are also relevant to computer…
We study the computational complexity of approximating the partition function of the ferromagnetic Ising model with the external field parameter $\lambda$ on the unit circle in the complex plane. Complex-valued parameters for the Ising…
Approximate Natural Gradient Descent (NGD) methods are an important family of optimisers for deep learning models, which use approximate Fisher information matrices to pre-condition gradients during training. The empirical Fisher (EF)…
We investigate the Pad\'e approximation method for the analytic continuation of numerical data and its ability to access, from the Euclidean propagator, both the spectral function and part of the physical information hidden in the second…
Despite the widespread use and success of machine-learning techniques for detecting phase transitions from data, their working principle and fundamental limits remain elusive. Here, we explain the inner workings and identify potential…
Variational inference, such as the mean-field (MF) approximation, requires certain conjugacy structures for efficient computation. These can impose unnecessary restrictions on the viable prior distribution family and further constraints on…
We present a general, rigorous theory of partition function zeros for lattice spin models depending on one complex parameter. First, we formulate a set of natural assumptions which are verified for a large class of spin models in a…
Phase-space representations based on coherent states (P, Q, Wigner) have been successful in the creation of stochastic differential equations (SDEs) for the efficient stochastic simulation of high dimensional quantum systems. However many…
We derive a single pass algorithm for computing the gradient and Fisher information of Vecchia's Gaussian process loglikelihood approximation, which provides a computationally efficient means for applying the Fisher scoring algorithm for…
We extend the renormalization group transformation based on the two-lattice matching to the complex inverse temperature plane for Dyson's hierarchical Ising model. We consider values of the dimensional parameter above, below and exactly at…
In this paper, a mixed high order finite difference scheme-Pad\'{e} approximation method is applied to obtain numerical solution of the Riesz fractional advection-dispersion equation. This method is based on the high order finite difference…
We consider the problems of clustering, classification, and visualization of high-dimensional data when no straightforward Euclidean representation exists. Typically, these tasks are performed by first reducing the high-dimensional data to…
In identification of dynamical systems, the prediction error method using a quadratic cost function provides asymptotically efficient estimates under Gaussian noise and additional mild assumptions, but in general it requires solving a…
We discuss a numerical analysis employing the density of partition function zeroes which permits effective distinction between phase transitions of first and second order, elucidates crossover between such phase transitions and gives a new…
We show that it is possible to determine the locus of Fisher zeroes in the thermodynamic limit for the Ising model on planar (``fat'') phi4 random graphs and their dual quadrangulations by matching up the real part of the high and low…
We consider the problem of computing the partition function $\sum_x e^{f(x)}$, where $f: \{-1, 1\}^n \longrightarrow {\Bbb R}$ is a quadratic or cubic polynomial on the Boolean cube $\{-1, 1\}^n$. In the case of a quadratic polynomial $f$,…