Lee–Yang zeros and two-time spin correlation function

Gnatenko, Kh. P.; Kargol, Alina; Tkachuk, V. M.

doi:10.1016/j.physa.2018.06.103

Cited by 18 publications

(43 citation statements)

References 41 publications

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“…These ideas now form the theoretical basis of phase transitions in interacting many-body systems. However, while partition function zeros for a long time were considered a purely theoretical concept, recent works have shown that they can also be determined experimentally [35][36][37][38][39][40][41][42][43].…”

Section: A the Ising Model And Lee-yang Zerosmentioning

confidence: 99%

“…In addition to these theoretical developments, partition function zeros have been determined in several recent experiments [35][36][37][38][39] and additional proposals for their detection have been developed [40][41][42][43]. In the approach that we follow here, the partition function zeros are extracted from the fluctuations of the thermodynamic observable that couples to the control parameter, for instance, magnetization and magnetic field, or energy and inverse temperature [9,32,44,45].…”

Section: Introductionmentioning

confidence: 99%

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Lee-Yang theory, high cumulants, and large-deviation statistics of the magnetization in the Ising model

2020

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We investigate the Ising model in one, two, and three dimensions using a cumulant method that allows us to determine the Lee-Yang zeros from the magnetization fluctuations in small lattices. By doing so with increasing system size, we are able to determine the convergence point of the Lee-Yang zeros in the thermodynamic limit and thereby predict the occurrence of a phase transition. The cumulant method is attractive from an experimental point of view since it uses fluctuations of measurable quantities, such as the magnetization in a spin lattice, and it can be applied to a variety of equilibrium and nonequilibrium problems. We show that the Lee-Yang zeros encode important information about the rare fluctuations of the magnetization. Specifically, by using a simple ansatz for the free energy, we express the large-deviation function of the magnetization in terms of Lee-Yang zeros. This result may hold for many systems that exhibit a first-order phase transition.

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Section: A the Ising Model And Lee-yang Zerosmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Lee-Yang theory, high cumulants, and large-deviation statistics of the magnetization in the Ising model

2020

View full text Add to dashboard Cite

show abstract

“…However, while partition function zeros for a long time were considered a purely theoretical concept, recent works have shown that they can also be determined experimentally. [35][36][37][38][39][40][41][42][43]…”

Section: Lee-yang Theory a The Ising Model And Lee-yang Zerosmentioning

confidence: 99%

“…[32][33][34] In addition to these theoretical developments, partition function zeros have been determined in several recent experiments [35][36][37][38][39] and additional proposals for their detection have been developed. [40][41][42][43] In the approach that we follow here, the partition function zeros are extracted from the fluctuations of the thermodynamic observable that couples to the control parameter, for instance, magnetization and magnetic field, or energy and inverse temperature. 9,32,44,45 The scheme is attractive from an experimental point of view since it makes it possible to explore phase transitions by measuring fluctuatuation in small systems, even for systems that are away from criticality.…”

Section: Introductionmentioning

confidence: 99%

Lee-Yang theory, high cumulants, and large-deviation statistics of the magnetization in the Ising model

Deger,

Brange,

Flindt

2020

Preprint

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We investigate the Ising model in one, two, and three dimensions using a cumulant method that allows us to determine the Lee-Yang zeros from the magnetization fluctuations in small lattices. By doing so with increasing system size, we are able to determine the convergence point of the Lee-Yang zeros in the thermodynamic limit and thereby predict the occurrence of a phase transition. The cumulant method is attractive from an experimental point of view since it uses fluctuations of measurable quantities, such as the magnetization in a spin lattice, and it can be applied to a variety of equilibrium and non-equilibrium problems. We show that the Lee-Yang zeros encode important information about the rare fluctuations of the magnetization. Specifically, by using a simple ansatz for the free energy, we express the large-deviation function of the magnetization in terms of Lee-Yang zeros. This result may hold for many systems that exhibit a first-order phase transition.

show abstract

“…Recently, partition function zeros were measured using carefully engineered nano-structures involving the precession of interacting molecular spins [17][18][19], Cooper pair tunneling in superconducting devices [20][21][22], or fermionic atoms in driven optical lattices [23]. In parallel with these experiments, several theoretical proposals have been put forward for the detection of partition function zeros [24][25][26][27][28]. These advances motivate a number of questions, which now should be addressed.…”

mentioning

confidence: 99%

Determination of universal critical exponents using Lee-Yang theory

Deger

Flindt

2019

Phys. Rev. Research

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Lee-Yang zeros are complex values of an external control parameter at which the partition function vanishes for a many-body system of finite size. In the thermodynamic limit, the Lee-Yang zeros approach the critical value on the real-axis where a phase transition occurs. Partition function zeros have for many years been considered a purely theoretical concept, however, the situation is changing now as Lee-Yang zeros have been determined in several recent experiments. Motivated by these developments, we here devise a direct pathway from measurements of partition function zeros to the determination of critical points and universal critical exponents of continuous phase transitions. To illustrate the feasibility of our approach, we extract the critical exponents of the Ising model in two and three dimensions from the fluctuations of the total energy and the magnetization in surprisingly small lattices. Importantly, the critical exponents can be determined even if the system is away from the phase transition, for example at a high temperature. As such, our method provides an intriguing perspective for investigations of phase transitions that may be hard to reach experimentally, for instance at very low temperatures or at very high pressures.

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Lee–Yang zeros and two-time spin correlation function

Cited by 18 publications

References 41 publications

Lee-Yang theory, high cumulants, and large-deviation statistics of the magnetization in the Ising model

Lee-Yang theory, high cumulants, and large-deviation statistics of the magnetization in the Ising model

Lee-Yang theory, high cumulants, and large-deviation statistics of the magnetization in the Ising model

Determination of universal critical exponents using Lee-Yang theory

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