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Related papers: Partition function zeros of aperiodic Ising models

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We present a numerical calculation of the Lee-Yang and Fisher zeros of the 2D Ising model using multi-point Pad\'{e} approximants. We perform simulations for the 2D Ising model with ferromagnetic couplings both in the absence and in the…

High Energy Physics - Lattice · Physics 2024-04-16 Simran Singh , Massimo Cipressi , Francesco Di Renzo

We study the q-dependent susceptibility chi(q) of a Z-invariant ferromagnetic Ising model on a Penrose tiling, as first introduced by Korepin using de Bruijn's pentagrid for the rapidity lines. The pair-correlation function for this model…

Statistical Mechanics · Physics 2015-06-24 Helen Au-Yang , Jacques H. H. Perk

We provide a simple characterization of the critical temperature for the Ising model on an arbitrary planar doubly periodic weighted graph. More precisely, the critical inverse temperature \beta for a graph G with coupling constants…

Mathematical Physics · Physics 2014-12-18 David Cimasoni , Hugo Duminil-Copin

A general numerical method is presented to locate the partition function zeros in the complex beta plane for large lattice sizes. We apply this method to the 2D Ising model and results are reported for square lattice sizes up tp L=64. We…

Statistical Mechanics · Physics 2009-10-30 Nelson A. Alves , J. R. Drugowich de Felicio , Ulrich H. E. Hansmann

We study the spectral curves of dimer models on periodic Fisher graphs, obtained from a ferromagnetic Ising model on $\mathbb{Z}^2$. The spectral curve is defined by the zero locus of the determinant of a modified weighted adjacency matrix.…

Complex Variables · Mathematics 2012-04-13 Zhongyang Li

The Lee-Yang theorem for the zeroes of the partition function is not strictly applicable to quantum systems because the zeroes are defined in units of the fugacity $e^{h\Delta\tau}$, and the Euclidean-time lattice spacing $\Delta\tau$ can…

Statistical Mechanics · Physics 2009-11-13 P. R. Crompton

We consider several aspects of non-periodic Ising models in one and two dimensions. Here we are not interested in random systems, but rather in models with intrinsic long-range aperiodic order. The most prominent examples in one dimension…

Condensed Matter · Physics 2007-05-23 Uwe Grimm , Michael Baake

Finite temperature density functional theory requires representations for the internal energy, entropy, and free energy as functionals of the local density field. A central formal difficulty for an orbital-free representation is…

Statistical Mechanics · Physics 2011-05-12 James W. Dufty , S. B. Trickey

In this work we study the recently developed parametrized partition function formulation and show how we can infer the thermodynamic properties of fermions based on numerical simulation of bosons and distinguishable particles at various…

Quantum Gases · Physics 2023-06-07 Yunuo Xiong , Hongwei Xiong

Using the monomer--dimer representation of the lattice Schwinger model, with $N_f =1$ Wilson fermions in the strong--coupling regime ($\beta=0$), we evaluate its partition function, $Z$, exactly on finite lattices. By studying the zeroes of…

High Energy Physics - Lattice · Physics 2009-10-22 F. Karsch , E. Meggiolaro , L. Turko

This paper is devoted to the study of the flatness property of linear time-invariant fractional systems. In the framework of polynomial matrices of the fractional derivative operator, we give a characterization of fractionally flat outputs…

Computational Physics · Physics 2015-09-10 Stéphane Victor , Pierre Melchior , Jean Lévine , Alain Oustaloup

Although the physical properties of the 2D and 1D Ising models are quite different, we point out an interesting connection between their complex-temperature phase diagrams. We carry out an exact determination of the complex-temperature…

High Energy Physics - Lattice · Physics 2009-10-28 Victor Matveev , Robert Shrock

We study the complexity of approximating the partition function $Z_{\mathrm{Ising}}(G; \beta)$ of the Ising model in terms of the relation between the edge interaction $\beta$ and a parameter $\Delta$ which is an upper bound on the maximum…

Computational Complexity · Computer Science 2022-04-11 Andreas Galanis , Leslie Ann Goldberg , Andrés Herrera-Poyatos

We investigate the distribution of zeros of the partition function of the two- and three-dimensional symmetric $\pm J$ Ising spin glasses on the complex field plane. We use the method to analytically implement the idea of numerical transfer…

Disordered Systems and Neural Networks · Physics 2008-08-04 Yoshiki Matsuda , Hidetoshi Nishimori , Koji Hukushima

We extend the circle theorem on the zeros of the partition function to a continuum system. We also calculate the exact zeros of the partition function for a finite system where the probability distribution for the order parameter is given…

Condensed Matter · Physics 2007-05-23 Koo-Chul Lee

The problem of N interacting spins on a lattice is equivalent to one of N clusters linked in a specific manner. The energy of any configuration of spins can be expressed in terms of the energy levels of this cluster. A new expression is…

Statistical Mechanics · Physics 2007-05-23 T. R. S. Prasanna

We explore connections between the phenomenon of correlation decay and the location of Lee-Yang and Fisher zeros for various spin systems. In particular we show that, in many instances, proofs showing that weak spatial mixing on the Bethe…

Computational Complexity · Computer Science 2022-08-05 Jingcheng Liu , Alistair Sinclair , Piyush Srivastava

We represent a general procedure for calculating the partition function of an Ising model on a one dimensional Fibonacci lattice in presence of magnetic field.This partition function can be written as a sum of partition functions of usual…

Statistical Mechanics · Physics 2007-05-23 Susanta Bhattacharya , Samir K. Paul

The distribution of partition function zeros is studied for the $\pm J$ model of spin glasses on the Bethe lattice. We find a relation between the distribution of complex cavity fields and the density of zeros, which enables us to obtain…

Disordered Systems and Neural Networks · Physics 2010-06-16 Yoshiki Matsuda , Markus Mueller , Hidetoshi Nishimori , Tomoyuki Obuchi , Antonello Scardicchio

In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact…

Mathematical Physics · Physics 2015-04-16 Grzegorz Siudem , Agata Fronczak , Piotr Fronczak