scholarly journals Anisotropic tensor renormalization group

2020 ◽  
Vol 102 (5) ◽  
Author(s):  
Daiki Adachi ◽  
Tsuyoshi Okubo ◽  
Synge Todo
Keyword(s):  
Renormalization Group ◽  
Anisotropic Tensor

scholarly journals Restoration of chiral symmetry in cold and dense Nambu-Jona-Lasinio model with tensor renormalization group

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shinichiro Akiyama ◽  
Yoshinobu Kuramashi ◽  
Takumi Yamashita ◽  
Yusuke Yoshimura
Keyword(s):  
Phase Transition ◽  
Renormalization Group ◽  
Chiral Symmetry ◽  
Chiral Condensate ◽  
Dense Region ◽  
Chiral Phase ◽  
Chiral Phase Transition ◽  
First Order ◽  
Anisotropic Tensor ◽  
Fermion Action

Abstract We analyze the chiral phase transition of the Nambu-Jona-Lasinio model in the cold and dense region on the lattice, developing the Grassmann version of the anisotropic tensor renormalization group algorithm. The model is formulated with the Kogut-Susskind fermion action. We use the chiral condensate as an order parameter to investigate the restoration of the chiral symmetry. The first-order chiral phase transition is clearly observed in the dense region at vanishing temperature with μ/T ∼ O(103) on a large volume of V = 10244. We also present the results for the equation of state.

scholarly journals Cost reduction of the bond-swapping part in an anisotropic tensor renormalization group

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Hideaki Oba
Keyword(s):  
Free Energy ◽  
Renormalization Group ◽  
Energy Density ◽  
Cost Reduction ◽  
Free Energy Density ◽  
Order Tensor ◽  
Computational Costs ◽  
Elapsed Time ◽  
Value Decomposition ◽  
Anisotropic Tensor

Abstract The bottleneck part of an anisotropic tensor renormalization group (ATRG) is a bond-swapping part that consists of a contraction of two tensors and a partial singular value decomposition of a matrix, and their computational costs are $O(\chi^{2d+1})$, where $\chi$ is the maximum bond dimension and $d$ is the dimensionality of the system. We propose an alternative method for the bond-swapping part and it scales with $O(\chi^{\max(d+3,7)})$, though the total cost of ATRG with the method remains $O(\chi^{2d+1})$. Moreover, the memory cost of the whole algorithm can be reduced from $O(\chi^{2d})$ to $O(\chi^{\max(d+1,6)})$. We examine ATRG with or without the proposed method in the 4D Ising model and find that the free energy density of the proposed algorithm is consistent with that of the original ATRG while the elapsed time is significantly reduced. We also compare the proposed algorithm with a higher-order tensor renormalization group (HOTRG) and find that the value of the free energy density of the proposed algorithm is lower than that of HOTRG in the fixed elapsed time.

The renormalization group and ultraviolet asymptotics

1979 ◽  
Vol 129 (11) ◽  
pp. 407 ◽  
Author(s):  
A.A. Vladimirov ◽  
D.V. Shirkov
Keyword(s):  
Renormalization Group

Phenomenological Renormalization Group and Cluster Approximation

2014 ◽  
Vol 59 (7) ◽  
pp. 655-662
Author(s):  
O. Borisenko ◽  
◽  
V. Chelnokov ◽  
V. Kushnir ◽  
◽  
...  
Keyword(s):  
Renormalization Group ◽  
Cluster Approximation ◽  
Phenomenological Renormalization

Renormalization Group

2020 ◽  
Author(s):  
Giuseppe Benfatto ◽  
Giovanni Gallavotti
Keyword(s):  
Renormalization Group

The Non-Causal Character of Renormalization Group Explanations

2018 ◽  
Author(s):  
Margaret Morrison
Keyword(s):  
Probability Theory ◽  
Renormalization Group ◽  
Dynamical Systems ◽  
Recent Literature ◽  
Mathematical Explanation ◽  
Causal Status ◽  
Physical Information ◽  
The Relationship ◽  
Structural Aspects

After reviewing some of the recent literature on non-causal and mathematical explanation, this chapter develops an argument as to why renormalization group (RG) methods should be seen as providing non-causal, yet physical, information about certain kinds of systems/phenomena. The argument centres on the structural character of RG explanations and the relationship between RG and probability theory. These features are crucial for the claim that the non-causal status of RG explanations involves something different from simply ignoring or “averaging over” microphysical details—the kind of explanations common to statistical mechanics. The chapter concludes with a discussion of the role of RG in treating dynamical systems and how that role exemplifies the structural aspects of RG explanations which in turn exemplifies the non-causal features.

scholarly journals Renormalization group study of superfluid phase transition: Effect of compressibility

2020 ◽  
Vol 102 (2) ◽  
Author(s):  
Michal Dančo ◽  
Michal Hnatič ◽  
Tomáš Lučivjanský ◽  
Lukáš Mižišin
Keyword(s):  
Phase Transition ◽  
Renormalization Group ◽  
Superfluid Phase ◽  
Transition Effect
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