scholarly journals Use of the Complex Zeros of the Partition Function to Investigate the Critical Behavior of the Generalized Interacting Self-Avoiding Trail Model

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 153
Author(s):  
Damien Foster ◽  
Ralph Kenna ◽  
Claire Pinettes
Keyword(s):  
Phase Transitions ◽  
Partition Function ◽  
Critical Behavior ◽  
Finite Size ◽  
The Self ◽  
Partition Function Zeros ◽  
Adsorption Transition ◽  
Function Zeros ◽  
Complex Zeros ◽  
Self Avoiding Walk

The complex zeros of the canonical (fixed walk-length) partition function are calculated for both the self-avoiding trails model and the vertex-interacting self-avoiding walk model, both in bulk and in the presence of an attractive surface. The finite-size behavior of the zeros is used to estimate the location of phase transitions: the collapse transition in the bulk and the adsorption transition in the presence of a surface. The bulk and surface cross-over exponents, ϕ and ϕ S , are estimated from the scaling behavior of the leading partition function zeros.

scholarly journals Many-body thermodynamics on quantum computers via partition function zeros

2021 ◽  
Vol 7 (34) ◽  
pp. eabf2447
Author(s):  
Akhil Francis ◽  
Daiwei Zhu ◽  
Cinthia Huerta Alderete ◽  
Sonika Johri ◽  
Xiao Xiao ◽  
...  
Keyword(s):  
Phase Transitions ◽  
Partition Function ◽  
Quantum Computers ◽  
Partition Functions ◽  
Chain Model ◽  
Many Body ◽  
Partition Function Zeros ◽  
Many Body Systems ◽  
Classical Computing ◽  
Function Zeros

Partition functions are ubiquitous in physics: They are important in determining the thermodynamic properties of many-body systems and in understanding their phase transitions. As shown by Lee and Yang, analytically continuing the partition function to the complex plane allows us to obtain its zeros and thus the entire function. Moreover, the scaling and nature of these zeros can elucidate phase transitions. Here, we show how to find partition function zeros on noisy intermediate-scale trapped-ion quantum computers in a scalable manner, using the XXZ spin chain model as a prototype, and observe their transition from XY-like behavior to Ising-like behavior as a function of the anisotropy. While quantum computers cannot yet scale to the thermodynamic limit, our work provides a pathway to do so as hardware improves, allowing the future calculation of critical phenomena for systems beyond classical computing limits.

scholarly journals Partition Function Zeros at First-Order Phase Transitions: A General Analysis

2004 ◽  
Vol 251 (1) ◽  
pp. 79-131 ◽  
Author(s):  
M. Biskup ◽  
C. Borgs ◽  
J.T. Chayes ◽  
L.J. Kleinwaks ◽  
R. Koteck�
Keyword(s):  
Phase Transitions ◽  
Partition Function ◽  
General Analysis ◽  
Partition Function Zeros ◽  
First Order ◽  
Function Zeros ◽  
First Order Phase
Sign in / Sign up

Export Citation Format

Share Document