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I derive a formulation of the 2-dimensional critical Ising model on non-uniform simplicial lattices. Surprisingly, the derivation leads to a set of geometric constraints that a lattice must satisfy in order for the model to have a…

High Energy Physics - Theory · Physics 2023-09-06 Evan Owen

In this paper we present a new solution of the star-triangle relation having positive Boltzmann weights. The solution defines an exactly solvable two-dimensional Ising-type (edge interaction) model of statistical mechanics where the local…

High Energy Physics - Theory · Physics 2023-11-14 Vladimir V. Bazhanov , Sergey M. Sergeev

The one-dimensional Ising model with its connections to several physical concepts plays a vital role in comprehension of several principles, phenomena and numerical methods. The Hamiltonian of a coupled one-dimensional dissipative spin…

The two-dimensional Ising model is the simplest model of statistical mechanics exhibiting a second order phase transition. While in absence of magnetic field it is known to be solvable on the lattice since Onsager's work of the forties,…

High Energy Physics - Theory · Physics 2009-11-10 Gesualdo Delfino

In 1944 Lars Onsager published the exact partition function of the ferromagnetic Ising model on the infinite square lattice in terms of a definite integral. Only in the literature of the last decade, however, has it been recast in terms of…

Statistical Mechanics · Physics 2021-09-01 Gandhimohan M. Viswanathan

We show how to compute the exact partition function for lattice statistical-mechanical models whose Boltzmann weights obey a special "crossing" symmetry. The crossing symmetry equates partition functions on different trivalent graphs,…

Statistical Mechanics · Physics 2015-06-12 Steven H. Simon , Paul Fendley

We introduce an intermediate quantum computing model built from translation-invariant Ising-interacting spins. Despite being non-universal, the model cannot be classically efficiently simulated unless the polynomial hierarchy collapses.…

Quantum Physics · Physics 2017-02-01 Xun Gao , Sheng-Tao Wang , Lu-Ming Duan

The presence of long-range quantum spin correlations underlies a variety of physical phenomena in condensed matter systems, potentially including high-temperature superconductivity. However, many properties of exotic strongly correlated…

We study the approximability of computing the partition functions of two-state spin systems. The problem is parameterized by a $2\times 2$ symmetric matrix. Previous results on this problem were restricted either to the case where the…

Computational Complexity · Computer Science 2025-08-19 Yumou Fei , Leslie Ann Goldberg , Pinyan Lu

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

Determining properties of ground states of spin Hamiltonians remains a topic of central relevance connecting disciplines of mathematical, theoretical and applied physics. In the last few decades, ground state properties of physical systems…

Quantum Physics · Physics 2021-12-28 Jacob Biamonte

The one-dimensional transverse Ising model is a paradigmatic example of quantum criticality. In spin-orbit coupled systems, however, effective Ising interactions arise alongside bond-dependent couplings such as Kitaev ($K$) and $\Gamma$…

Strongly Correlated Electrons · Physics 2026-03-17 Mandev Bhullar , Philip Richard , Hae-Young Kee

We present detailed analytical calculations for an 1D Ising ring of arbitrary number of spin-1/2 particles, in order to reveal entanglement properties of the stationary states. We show that the ground state and specific eigenstates of the…

Quantum Physics · Physics 2007-05-23 P. Štelmachovič , V. Bužek

It is shown that the canonical problem of classical statistical thermodynamics, the computation of the partition function, is in the case of +/-J Ising spin glasses a particular instance of certain simple sums known as quadratically signed…

Quantum Physics · Physics 2007-05-23 Daniel A. Lidar

The universal scaling function of the square lattice Ising model in a magnetic field is obtained numerically via Baxter's variational corner transfer matrix approach. The high precision numerical data is in perfect agreement with the…

Statistical Mechanics · Physics 2009-02-02 Vladimir V. Mangazeev , Murray T. Batchelor , Vladimir V. Bazhanov , Michael Yu. Dudalev

We present a comprehensive comparison of spin and energy dynamics in quantum and classical spin models on different geometries, ranging from one-dimensional chains, over quasi-one-dimensional ladders, to two-dimensional square lattices.…

Statistical Mechanics · Physics 2021-08-27 Dennis Schubert , Jonas Richter , Fengping Jin , Kristel Michielsen , Hans De Raedt , Robin Steinigeweg

Even simplified models of quantum many-body systems can be difficult to analyse. However, taking inspiration from the foundations of physics, one may wonder whether there are practical advantages to constructing alternative beyond-quantum…

Quantum Physics · Physics 2026-05-01 Sahar Atallah , Peter Carrekmor , Michael Garn , Yukuan Tao , Shashank Virmani

We consider generalized quantum Ising models, including those which could describe disordered materials or quantum annealers, and we prove that for all temperatures above a system-size independent threshold the path integral Monte Carlo…

Quantum Physics · Physics 2025-07-16 Elizabeth Crosson , Samuel Slezak

A scheme for measuring complex temperature partition functions of Ising models is introduced. In the context of ordered qubit registers this scheme finds a natural translation in terms of global operations, and single particle measurements…

Quantum Physics · Physics 2013-11-19 S. Iblisdir , M. Cirio , O. Boada , G. K. Brennen

Studying the zeroes of partition functions in the space of complex control parameters allows to understand formally how critical behavior of a many-body system can arise in the thermodynamic limit despite various no-go theorems for finite…

Quantum Physics · Physics 2019-08-28 Abijith Krishnan , Markus Schmitt , Roderich Moessner , Markus Heyl