A note on Lee–Yang zeros in the negative half-plane

Lebowitz, Joel L.; Scaramazza, Jasen A.

doi:10.1088/0953-8984/28/41/414004

Cited by 6 publications

(9 citation statements)

References 41 publications

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“…Thus transition probed by the local spin-spin correlation function (10) is due to the imaginary part iπ/2 added to the nearest-neighbor exchange coupling. For the dual Hamiltoinian (6) the problem reduced again to evaluation of Z(h + iπ/2).…”

Section: Disorder Line and Complex Magnetic Fieldmentioning

confidence: 99%

“…The original analysis of the ferromagnetic Ising model created a huge impact and a vast literature extending results 1 on other models and/or non-equilibrium cases. For a very limited list of references see, e.g., [2][3][4][5][6] .…”

Section: Introduction and Motivation Disorder Line In The Classicmentioning

confidence: 99%

“…known as the Anisotropic Next-Nearest Neighbor Ising (ANNNI) chain. 13 The nonlocal string-string correlation function of the Ising chain ( 1) is a conventional two-point correlation function of the dual ANNNI model (6):…”

Section: Introduction and Motivation Disorder Line In The Classical I...mentioning

confidence: 99%

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Infinite cascades of phase transitions in the classical Ising chain

Timonin

Chitov

2017

Phys. Rev. E

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We report the new exact results on one of the best studied models in statistical physics: the classical antiferromagnetic Ising chain in a magnetic field. We show that the model possesses an infinite cascade of thermal phase transitions (also known as "disorder lines" or geometric phase transitions). The phase transition is signalled by a change of asymptotic behavior of the nonlocal string-string correlation functions when their monotonous decay becomes modulated by incommensurate oscillations. The transitions occur for rarefied (m-periodic) strings with arbitrary odd m. We propose a duality transformation which maps the Ising chain onto the m-leg Ising tube with nearest-neighbor couplings along the legs and the plaquette four-spin interactions of adjacent legs. Then the m-string correlation functions of the Ising chain are mapped onto the two-point spin-spin correlation functions along the legs of the m-leg tube. We trace the origin of these cascades of phase transitions to the lines of the Lee-Yang zeros of the Ising chain in m-periodic complex magnetic field, allowing us to relate these zeros to the observable (and potentially measurable) quantities.

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Section: Disorder Line and Complex Magnetic Fieldmentioning

confidence: 99%

Section: Introduction and Motivation Disorder Line In The Classicmentioning

confidence: 99%

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Infinite cascades of phase transitions in the classical Ising chain

Timonin

Chitov

2017

Phys. Rev. E

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“…Generalizations of this program to higher spins and Heisenberg models soon followed [3][4][5][6][7][8][9][10]. In the next decades, results on other geometries and interactions, in particular antiferromagnetic Ising models, became available [11][12][13][14][15][16][17][18]. The endeavor of characterizing complex zeros of real polynomials with positive coeffi- * lichengshu272@gmail.com cients has attracted interest from the mathematics community alike [19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Lee-Yang zeros in the Rydberg atoms

Li¹,

Yang²

2022

Preprint

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Lee-Yang (LY) zeros play a fundamental role in the formulation of statistical physics in terms of (grand) partition functions, and assume theoretical significance for the phenomenon of phase transitions. In this paper, motivated by recent progress in cold Rydberg atom experiments, we explore the LY zeros in classical Rydberg blockade models. We prove that all the LY zeros are real for such models with arbitrary blockade radii, and show how the zeros redistribute as one interpolates between nearest-and next-nearest-neighbor blockade. We also discuss possible experimental measurements of these zeros.

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“…In some cases such as monomer-dimer systems [31] or complex networks of Ising spins [32,33] the LYT is found to be violated through the occurrence of an accumulation of zeros on the negative real axis [34] instead of the unit circle. Recently, the LYT has been implemented to analyze the phase diagram of Quantum Chromodynamics (QCD) on the lattice [35][36][37][38].…”

mentioning

confidence: 99%

Condensation of Lee-Yang zeros in scalar field theory

et al. 2017

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We show that, at the critical temperature, there is a class of Lee-Yang zeros of the partition function in a general scalar field theory, which location scales with the size of the system with a characteristic exponent expressed in terms of the isothermal critical exponent δ. In the thermodynamic limit the zeros belonging to this class condense to the critical point ζ=1 on the real axis in the complex fugacity plane while the complementary set of zeros (with Reζ<1) covers the unit circle. Although the aforementioned class degenerates to a single point for an infinite system, when the size is finite it contributes significantly to the partition function and reflects the self-similar structure (fractal geometry, scaling laws) of the critical system. This property opens up the perspective to formulate finite-size scaling theory in effective QCD, near the chiral critical point, in terms of the location of Lee-Yang zeros.

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A note on Lee–Yang zeros in the negative half-plane

Cited by 6 publications

References 41 publications

Infinite cascades of phase transitions in the classical Ising chain

Infinite cascades of phase transitions in the classical Ising chain

Lee-Yang zeros in the Rydberg atoms

Condensation of Lee-Yang zeros in scalar field theory

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