Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2303.09039 · International Journal of Modern Physics E

Classification of pairing phase transition in the hot nucleus

Yuhang Gao, Yanlong Lin, Lang Liu

Published Sep 1, 2023• 5 citations
arXivHTMLPDF

Abstract

The hot nucleus [Formula: see text] is investigated using covariant density functional theory, where the shell-model-like approach treats the pairing correlation. Lee–Yang’s theorem is applied to classify the pairing phase transition by analyzing the distribution of zeros of the partition function in the complex temperature plane. The distribution of zeros of the partition function converges with increasing particle numbers and illustrates the characteristics of the phase transition. In our calculations, we determine the first-order of the phase transition near the critical temperature. Different seniority states show the pairing phase transition from a superfluid to a normal phase, ranging from fully paired states to completely unpaired states.

DOI
10.1142/s0218301323500507

Related papers

Pairing phase transition in the odd-A nuclei: identification and classification

Yumeng Wang, Yuhang Gao, Lang Liu

The investigation into the pairing phase transition in the odd-A nucleus 161Dy utilizes a sophisticated blend of covariant density functional theory and the shell-model-like approach. It is discerned that variations in thermodynamic quantities at the critical temperature do not exclusively align with pairing phase transitions. The presence of an S-shaped heat capacity curve, often interpreted as an indication of such transitions, does not offer a definitive confirmation. Additional factors, including the blocking effect, can modify the heat capacity curve and impede the transition process. The pairing phase transition in 161Dy, occurring around 0.7 to 1.0 MeV, is unequivocally characterized as a first-order transition. Furthermore, an exploration into the impact of varying strengths of pairing correlations on these transitions reveals a nonlinear relationship, adding complexity to the transition dynamics.

arXiv:2408.00423•Aug 1, 2024•0 citations

Analytic Properties of the Partition Function near the Normal-to-Superconducting Phase Transition

Roger Balian, James S. Langer

It is shown that the grand partition function for a superconductor has analytic properties near the transition point in the complex temperature plane similar to those described by Lee and Yang in their statistical theory of condensation. The normal and superconducting regions of the complex plane are separated by a line of zeroes which, in the limit of infinite volume, becomes a natural boundary.

Physical Review•Nov 1, 1963•3 citations

Critical Behavior of Pair Correlation Function in Ising Ferromagnets

Ryuzo Abe

Behavior of pair correlation function in Ising ferromagnets near the transition point is studied in two different ways. First, it is studied by means of the Lee-Yang theoremon the distribution of zeros of partition function. Secondly, a diagrammatic method is developed and a connection is discussed between the results obtained by these two different methods.

Progress of Theoretical Physics•Sep 1, 1967•28 citations

Lee-Yang theory of the two-dimensional quantum Ising model

Pascal M. Vecsei, José Luis Lado, Christian Flindt

Determining the phase diagram of interacting quantum many-body systems is an important task for a wide range of problems such as the understanding and design of quantum materials. For classical equilibrium systems, the Lee-Yang formalism provides a rigorous foundation of phase transitions, and these ideas have also been extended to the quantum realm. Here, we develop a Lee-Yang theory of quantum phase transitions that can include thermal fluctuations caused by a finite temperature, and it thereby provides a link between the classical Lee-Yang formalism and recent theories of phase transitions at zero temperature. Our methodology exploits analytic properties of the moment generating function of the order parameter in systems of finite size, and it can be implemented in combination with tensor-network calculations. Specifically, the onset of a symmetry-broken phase is signaled by the zeros of the moment generating function approaching the origin in the complex plane of a counting field that couples to the order parameter. Moreover, the zeros can be obtained by measuring or calculating the high cumulants of the order parameter. We determine the phase diagram of the two-dimensional quantum Ising model and thereby demonstrate the potential of our method to predict the critical behavior of two-dimensional quantum systems at finite temperatures.

arXiv:2204.08223•Physical review. B./Physical review. B•Aug 1, 2022•20 citations

Classification of Phase Transitions in Small Systems

Peter Borrmann, Oliver Mülken, Jens Harting

We present a classification scheme for phase transitions in finite systems like atomic and molecular clusters based on the Lee-Yang zeros in the complex temperature plane. In the limit of infinite particle numbers the scheme reduces to the Ehrenfest definition of phase transitions and gives the right critical indices. We apply this classification scheme to Bose-Einstein condensates in a harmonic trap as an example of a higher order phase transition in a finite system and to small Ar clusters.

arXiv:cond-mat/9909184•Physical Review Letters•Apr 17, 2000•131 citations

Distribution of Zeros of the Partition Function in the First and Second Order Phase Transitions: Extension of the Lee-Yang Theorem

Keiji Yamada, H. Nakano, Mamoru Yamashita

The distribution of zeros of the partition function for one-dimensional lattice system of generalized Ising spins with magnitude unity is studied, where it is assumed that the component spins interact with the nearest neighbours through a ferromagnetic coupling and each spin state has a certain degeneracy. The spin states are denoted by variable σ which can take either of three values, plus and minus unities and zero with the respective degeneracies, D(1), D(0) and D(-1), where it is assumed D(1) = D(-1). zeros of the partition function Z(ζ) of the system as exposed to an external magnetic field are studied on the ζ-plane, where ζ=exp(H) indicates the exponential function of the external field divided by temperature H and it is regarded as a complex number. The distribution of zeros is classified into three typical patterns, corresponding to the respective three regions on the plane of temperature(T) versus degneracy ratio (ρ=D(0)/D(1)): Zeros never lie on the unit circle in the region of larger ρ, all on the unit circle in the region of smaller ρ and only a part on the unit circle in the remaining region. On the basic of this result, it is expected in the case of two- or three-dimensional system that phase trasitions of first and second orders occur in tha cases of ρ larger and smaller than acritical calue ρc, respectively.

Progress of Theoretical Physics•May 1, 1981•6 citations
The hot nucleus [Formula: see text] is investigated using covariant density functional theory, where the shell-model-like approach treats the pairing correlation. Lee–Yang’s theorem is applied to classify the pairing phase transition by analyzing the distribution of zeros of the partition function in the complex temperature plane. The distribution of zeros of the partition function converges with increasing particle numbers and illustrates the characteristics of the phase transition. In our calculations, we determine the first-order of the phase transition near the critical temperature. Different seniority states show the pairing phase transition from a superfluid to a normal phase, ranging from fully paired states to completely unpaired states.
The investigation into the pairing phase transition in the odd-A nucleus 161Dy utilizes a sophisticated blend of covariant density functional theory and the shell-model-like approach. It is discerned that variations in thermodynamic quantities at the critical temperature do not exclusively align with pairing phase transitions. The presence of an S-shaped heat capacity curve, often interpreted as an indication of such transitions, does not offer a definitive confirmation. Additional factors, including the blocking effect, can modify the heat capacity curve and impede the transition process. The pairing phase transition in 161Dy, occurring around 0.7 to 1.0 MeV, is unequivocally characterized as a first-order transition. Furthermore, an exploration into the impact of varying strengths of pairing correlations on these transitions reveals a nonlinear relationship, adding complexity to the transition dynamics.
Determining the phase diagram of interacting quantum many-body systems is an important task for a wide range of problems such as the understanding and design of quantum materials. For classical equilibrium systems, the Lee-Yang formalism provides a rigorous foundation of phase transitions, and these ideas have also been extended to the quantum realm. Here, we develop a Lee-Yang theory of quantum phase transitions that can include thermal fluctuations caused by a finite temperature, and it thereby provides a link between the classical Lee-Yang formalism and recent theories of phase transitions at zero temperature. Our methodology exploits analytic properties of the moment generating function of the order parameter in systems of finite size, and it can be implemented in combination with tensor-network calculations. Specifically, the onset of a symmetry-broken phase is signaled by the zeros of the moment generating function approaching the origin in the complex plane of a counting field that couples to the order parameter. Moreover, the zeros can be obtained by measuring or calculating the high cumulants of the order parameter. We determine the phase diagram of the two-dimensional quantum Ising model and thereby demonstrate the potential of our method to predict the critical behavior of two-dimensional quantum systems at finite temperatures.
The distribution of zeros of the partition function for one-dimensional lattice system of generalized Ising spins with magnitude unity is studied, where it is assumed that the component spins interact with the nearest neighbours through a ferromagnetic coupling and each spin state has a certain degeneracy. The spin states are denoted by variable σ which can take either of three values, plus and minus unities and zero with the respective degeneracies, D(1), D(0) and D(-1), where it is assumed D(1) = D(-1). zeros of the partition function Z(ζ) of the system as exposed to an external magnetic field are studied on the ζ-plane, where ζ=exp(H) indicates the exponential function of the external field divided by temperature H and it is regarded as a complex number. The distribution of zeros is classified into three typical patterns, corresponding to the respective three regions on the plane of temperature(T) versus degneracy ratio (ρ=D(0)/D(1)): Zeros never lie on the unit circle in the region of larger ρ, all on the unit circle in the region of smaller ρ and only a part on the unit circle in the remaining region. On the basic of this result, it is expected in the case of two- or three-dimensional system that phase trasitions of first and second orders occur in tha cases of ρ larger and smaller than acritical calue ρc, respectively.