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Fisher zeros and correlation decay in the Ising model [article]

Jingcheng Liu, Alistair Sinclair, Piyush Srivastava
2018 arXiv   pre-print
Our main result shows that the zero-field Ising model has no Fisher zeros in a complex neighborhood of the entire region of parameters where the model exhibits correlation decay.  ...  We study the complex zeros of the partition function of the Ising model, viewed as a polynomial in the "interaction parameter"; these are known as Fisher zeros in light of their introduction by Fisher  ...  Thus, in the particular case of the zero eld Ising model, we are able to establish a tight connection between correlation decay and the absence of zeros.  ... 
arXiv:1807.06577v2 fatcat:2ocuko5pqvfn3geena2pinkxeu

Fisher zeros and correlation decay in the Ising model

Jingcheng Liu, Alistair Sinclair, Piyush Srivastava
2019 Journal of Mathematical Physics  
Our main result shows that the zero-field Ising model has no Fisher zeros in a complex neighborhood of the entire region of parameters where the model exhibits correlation decay.  ...  In this paper, we study the complex zeros of the partition function of the Ising model, viewed as a polynomial in the "interaction parameter"; these are known as Fisher zeros in light of their introduction  ...  :4 Fisher Zeros and Correlation Decay in the Ising Model give a deterministic algorithm for approximating the partition function of the Ising model for such β [27, 29] .  ... 
doi:10.1063/1.5082552 fatcat:wjhfdgld3ng5fiqoh73c6r57cu

Page 395 of Journal of Chemometrics Vol. 5, Issue 4 [page]

1991 Journal of Chemometrics  
In other cases the value was close to zero, accounting for the mean Fisher weight of only 0-97.  ...  The acoustic signals obtained in this study typically gave values between zero and ten.  ... 

Dimensional crossover and the link between thermodynamics and dynamics: the case of Ising models at complex temperature [article]

Sankhya Basu, Chris A. Hooley, Vadim Oganesyan
2020 arXiv   pre-print
We study dimensional crossover in Ising systems at complex temperatures by comparing three types of system: the infinite isotropic 2D Ising model; the infinite anisotropic 2D Ising model; and Ising ladders  ...  In particular we present evidence, from both tensor-network calculations and numerical evaluations based on the exact solution of the model, that the infinite anisotropic 2D Ising model exhibits long-range  ...  Dashed lines represent the expected location of Fisher zeros of the isotropic 2D Ising model 14 .  ... 
arXiv:2001.05475v2 fatcat:bh2hcj7745htjhbqzvk6lk4pmq

Coulomb and Liquid Dimer Models in Three Dimensions

David A. Huse, Werner Krauth, R. Moessner, S. L. Sondhi
2003 Physical Review Letters  
The non-bipartite FCC and Fisher lattices lack such a representation, and we find that these models have both confined and exponentially deconfined but no critical phases.  ...  , correlations, in excellent agreement with our large-scale Monte Carlo simulations.  ...  RM was in part supported by the Ministère de la Recherche et des Nouvelles Technologies with an ACI grant, and thanks the KITP for hospitality during part of this work.  ... 
doi:10.1103/physrevlett.91.167004 pmid:14611431 fatcat:kboeowd2mrh6jashj5pnaxlzyq

Noise limits on two-photon interferometric sensing [article]

Hamish Scott, Dominic Branford, Niclas Westerberg, Jonathan Leach, Erik M. Gauger
2021 arXiv   pre-print
When a photon interferes with itself while traversing a Mach-Zehnder inteferometer, the output port where it emerges is influenced by the phase difference between the interferometer arms.  ...  This allows for highly precise estimation of the path length difference (delay) but is extremely sensitive to phase noise.  ...  If the photons are independent, the Fisher information instead decays to zero.  ... 
arXiv:2106.13671v2 fatcat:5iicwud3krfz5jjjnefkqeojju

Spin–spin correlation in some excited states of the transverse Ising model

Anjan Kumar Chandra, Subinay Dasgupta
2007 Journal of Physics A: Mathematical and Theoretical  
We consider the transverse Ising model in one dimension with nearest-neighbour interaction and calculate exactly the longitudinal spin-spin correlation for a class of excited states.  ...  The result is that the correlation decays algebraically with distance (n) as 1/ n and is oscillatory or non-oscillatory depending on the magnitude of the transverse field.  ...  Acknowledgments The work of one author (AKC) was supported by UGC fellowship.  ... 
doi:10.1088/1751-8113/40/20/001 fatcat:y4tuauitdrd2zmmcfbjospawei

Random-exchange disorder in the spin-1/2XXZchain

Stephan Haas, Jose Riera, Elbio Dagotto
1993 Physical Review B (Condensed Matter)  
As the planar anisotropy is varied, the full zero-temperature phase diagram is obtained and compared with predictions of Doty and Fisher [Phys. Rev. B 45 , 2167 (1992)].  ...  The one-dimensional XXZ model is studied in the presence of disorder in the Heisenberg Exchange Integral.  ...  The observed decay in η z for δJ xy between J and 2J is due to ferromagnetic behavior in the real space spin-spin correlations. This anomaly is observed specially for anisotropies −1 < λ ≤ −0.5.  ... 
doi:10.1103/physrevb.48.13174 pmid:10007705 fatcat:67jebkbqr5ba7d4fhnuqqi7doa

Discontinuous transition in a boundary driven contact process

A Costa, R A Blythe, M R Evans
2010 Journal of Statistical Mechanics: Theory and Experiment  
This model exhibits waves of activity emanating from the active wall and, when the system is supercritical, propagating indefinitely as travelling (Fisher) waves.  ...  In the subcritical phase the activity is localised near the wall.  ...  One consequence of this rotation is that the spatial correlation length measured in the steady-state density profile of the DACP is a linear combination of the temporal and spatial correlations lengths  ... 
doi:10.1088/1742-5468/2010/09/p09008 fatcat:tmsim2oth5dttmmroo7rj76avm

Fisher zeros and persistent temporal oscillations in nonunitary quantum circuits

Sankhya Basu, Daniel P. Arovas, Sarang Gopalakrishnan, Chris A. Hooley, Vadim Oganesyan
2022 Physical Review Research  
anisotropic Ising model.  ...  Unlike the time crystals that have been found in unitary models, those that occur here are incommensurate with the drive frequency.  ...  underlying Fisher zeros in the thermodynamics of Ising ladders.  ... 
doi:10.1103/physrevresearch.4.013018 fatcat:rcfuacgdzrf43mydwrow5h43a4

Exact results for the Potts model in two dimensions

A. Hintermann, H. Kunz, F. Y. Wu
1978 Journal of statistical physics  
By considering the zeros of the partition function, we establish the following results for the Potts model on the square, triangular, and honeycomb lattices: (i) We show that there exists only one phase  ...  transition; (ii) we give an exact determination of the critical point; Off) we prove the exponential decay of the correlation functions, in one direction at least, for all temperatures above the critical  ...  For 0 < q < 4, conditions (A) and (B) of the Suzuki-Fisher theorem no longer hold and the locus of the zeros of ZN'(/3, z) is not known.  ... 
doi:10.1007/bf01011773 fatcat:rxcjy7dk6fc2jobqrgd5hfk34q

Persistence of power-law correlations in nonequilibrium steady states of gapped quantum spin chains

Jarrett L. Lancaster, Joseph P. Godoy
2019 Physical Review Research  
The magnetization, spin current, and spin-spin correlation functions are computed analytically in the thermodynamic limit at long times after the quench.  ...  For both types of systems, we find the persistence of power-law correlations despite the ground-state correlation functions exhibiting exponential decay.  ...  Naïvely applying the Fisher-Hartwig conjecture, the product of zeros and discontinuities results in a vanishing power-law factor.  ... 
doi:10.1103/physrevresearch.1.033104 fatcat:s4errnu6trafjdc7kaqmmhuwre

A simulation study of the decay of the pair correlation function in simple fluids

Marjolein Dijkstra, Robert Evans
2000 Journal of Chemical Physics  
In the case of the hard-sphere fluid, the ultimate decay of h(r) is oscillatory for all densities and we find that simulation results for the period and ͑exponential͒ decay length of the oscillations are  ...  Monte Carlo simulations are used to investigate the asymptotic decay of the total pairwise correlation function h(r) for some model fluids.  ...  In magnetism, spin-spin correlations can also exhibit different types of asymptotic decay and the analog of the cross over or Fisher-Widom ͑FW͒ line is well-known and is termed the disorder transition  ... 
doi:10.1063/1.480598 fatcat:fnpozmhu7zfc3b77hg2sqiino4

Fisher–Hartwig determinants, conformal field theory and universality in generalised XX models

J Hutchinson, N G Jones
2016 Journal of Statistical Mechanics: Theory and Experiment  
We give physical context to mathematical results for the entanglement entropy, and calculate the spin-spin correlation functions using the Fisher-Hartwig conjecture.  ...  These were studied by Keating and Mezzadri in the context of their relation to the Haar measures of the classical compact groups.  ...  Mezzadri and J. M. Robbins for helpful discussions. We thank J. P. Keating and R. Verresen for crucial remarks as well as comments on the manuscript.  ... 
doi:10.1088/1742-5468/2016/07/073103 fatcat:tycxtypv2nhxfi2jaodp634poy

Local quantum Fisher information and local quantum uncertainty in two qubit Heisenberg XYZ chain with Dzyaloshinskii Moriya interactions [article]

Soroush Haseli
2020 arXiv   pre-print
In this work we will study the Local quantum Fisher information and the local quantum uncertainty in two-qubit Heisenberg XYZ spin chain model with Dzyaloshinskii Moriya (DM) interaction in z direction  ...  Here we show that the DM interaction and spin interactions along the x, y, and z axis can increase and maintain local quantum Fisher information and local quantum uncertainty.  ...  This happens because thermal fluctuations only affect quantum correlations at temperatures above the characteristic temperature set by the gap energy, which is non-zero for a finite sized systems.  ... 
arXiv:2005.00425v1 fatcat:yxgjg2iembd6ljw6yvz46g2ad4
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