scholarly journals Solution of the sign problem in the Potts model at fixed fermion number

2018 ◽  
Vol 97 (11) ◽  
Author(s):  
Andrei Alexandru ◽  
Georg Bergner ◽  
David Schaich ◽  
Urs Wenger
Keyword(s):  
Potts Model ◽  
Fermion Number ◽  
Sign Problem

scholarly journals Spin models in complex magnetic fields: a hard sign problem

2018 ◽  
Vol 175 ◽  
pp. 07026 ◽  
Author(s):  
Philippe de Forcrand ◽  
Tobias Rindlisbacher
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Partition Function ◽  
External Field ◽  
Potts Model ◽  
Cluster Algorithm ◽  
Spin Models ◽  
Sign Problem ◽  
Special Cases ◽  
Severe Sign

Coupling spin models to complex external fields can give rise to interesting phenomena like zeroes of the partition function (Lee-Yang zeroes, edge singularities) or oscillating propagators. Unfortunately, it usually also leads to a severe sign problem that can be overcome only in special cases; if the partition function has zeroes, the sign problem is even representation-independent at these points. In this study, we couple the N-state Potts model in different ways to a complex external magnetic field and discuss the above mentioned phenomena and their relations based on analytic calculations (1D) and results obtained using a modified cluster algorithm (general D) that in many cases either cures or at least drastically reduces the sign-problem induced by the complex external field.

scholarly journals Normalizing flows and the real-time sign problem

2021 ◽  
Vol 103 (11) ◽  
Author(s):  
Scott Lawrence ◽  
Yukari Yamauchi
Keyword(s):  
Real Time ◽  
The Real ◽  
Sign Problem

scholarly journals A minimum energy optimization approach for simulations of the droplet wetting modes using the cellular Potts model

RSC Advances ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 1875-1882
Author(s):  
Ronghe Xu ◽  
Xiaoli Zhao ◽  
Liqin Wang ◽  
Chuanwei Zhang ◽  
Yuze Mao ◽  
...  
Keyword(s):  
Potts Model ◽  
Minimum Energy ◽  
Energy Optimization ◽  
Optimization Approach ◽  
Cellular Potts Model

An optimization approach based on the synthesis minimum energy was proposed for determining droplet wetting modes.

scholarly journals Complex Langevin calculations in QCD at finite density

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Yuta Ito ◽  
Hideo Matsufuru ◽  
Yusuke Namekawa ◽  
Jun Nishimura ◽  
Shinji Shimasaki ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Chemical Potential ◽  
Expansion Method ◽  
Finite Density ◽  
Fermi Sphere ◽  
Expectation Value ◽  
Sign Problem ◽  
Zero Momentum ◽  
Effective Theories ◽  
Severe Sign

Abstract We demonstrate that the complex Langevin method (CLM) enables calculations in QCD at finite density in a parameter regime in which conventional methods, such as the density of states method and the Taylor expansion method, are not applicable due to the severe sign problem. Here we use the plaquette gauge action with β = 5.7 and four-flavor staggered fermions with degenerate quark mass ma = 0.01 and nonzero quark chemical potential μ. We confirm that a sufficient condition for correct convergence is satisfied for μ/T = 5.2 − 7.2 on a 83 × 16 lattice and μ/T = 1.6 − 9.6 on a 163 × 32 lattice. In particular, the expectation value of the quark number is found to have a plateau with respect to μ with the height of 24 for both lattices. This plateau can be understood from the Fermi distribution of quarks, and its height coincides with the degrees of freedom of a single quark with zero momentum, which is 3 (color) × 4 (flavor) × 2 (spin) = 24. Our results may be viewed as the first step towards the formation of the Fermi sphere, which plays a crucial role in color superconductivity conjectured from effective theories.

scholarly journals Nontopological fractional fermion number in the Jackiw-Rossi model

2021 ◽  
Vol 103 (12) ◽  
Author(s):  
Caio Almeida ◽  
Alberto Alonso-Izquierdo ◽  
Rodrigo Fresneda ◽  
Juan Mateos Guilarte ◽  
Dmitri Vassilevich
Keyword(s):  
Fermion Number

scholarly journals Geometrical four-point functions in the two-dimensional critical Q-state Potts model: the interchiral conformal bootstrap

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yifei He ◽  
Jesper Lykke Jacobsen ◽  
Hubert Saleur
Keyword(s):  
Potts Model ◽  
Correlation Functions ◽  
Liouville Theory ◽  
Analytical Determination ◽  
Conformal Weight ◽  
Two Dimensional ◽  
Conformal Blocks ◽  
Conformal Bootstrap ◽  
Point Correlation

Abstract Based on the spectrum identified in our earlier work [1], we numerically solve the bootstrap to determine four-point correlation functions of the geometrical connectivities in the Q-state Potts model. Crucial in our approach is the existence of “interchiral conformal blocks”, which arise from the degeneracy of fields with conformal weight hr,1, with r ∈ ℕ*, and are related to the underlying presence of the “interchiral algebra” introduced in [2]. We also find evidence for the existence of “renormalized” recursions, replacing those that follow from the degeneracy of the field $$ {\Phi}_{12}^D $$ Φ 12 D in Liouville theory, and obtain the first few such recursions in closed form. This hints at the possibility of the full analytical determination of correlation functions in this model.

Erratum: The Potts model

1983 ◽  
Vol 55 (1) ◽  
pp. 315-315 ◽  
Author(s):  
F. Y. Wu
Keyword(s):  
Potts Model
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