scholarly journals Finite Size Scaling of the Higgs-Yukawa Model near the Gaussian Fixed Point

2016 ◽  
Author(s):  
Yen-Jen David Chu ◽  
Karl Jansen ◽  
Bastian Knippschild ◽  
C. -J. David Lin ◽  
Attila Nagy
Keyword(s):  
Fixed Point ◽  
Finite Size ◽  
Finite Size Scaling ◽  
Yukawa Model ◽  
Size Scaling

scholarly journals Finite-size scaling for four-dimensional Higgs-Yukawa model near the Gaussian fixed point

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
David Y.-J. Chu ◽  
Karl Jansen ◽  
Bastian Knippschild ◽  
C.-J. David Lin
Keyword(s):  
Fixed Point ◽  
Finite Size ◽  
Finite Size Scaling ◽  
Yukawa Model ◽  
Size Scaling

scholarly journals Finite-size Scaling of O(n) Systems at the Upper Critical Dimensionality*

2020 ◽  
Author(s):  
Jian-Ping Lv ◽  
Wanwan Xu ◽  
Yanan Sun ◽  
Kun Chen ◽  
Youjin Deng
Keyword(s):  
Fixed Point ◽  
Finite Size ◽  
Vector Model ◽  
Logarithmic Correction ◽  
Magnetic Fluctuations ◽  
Finite Size Scaling ◽  
Practical Applications ◽  
Size Scaling ◽  
Experimental Systems ◽  
Point Correlation

Abstract Logarithmic finite-size scaling of the O(n) universality class at the upper critical dimensionality (dc = 4) has a fundamental role in statistical and condensed-matter physics and important applications in various experimental systems. Here, we address this long-standing problem in the context of the n-vector model (n = 1, 2, 3) on periodic four-dimensional hypercubic lattices. We establish an explicit scaling form for the free energy density, which simultaneously consists of a scaling term for the Gaussian fixed point and another term with multiplicative logarithmic corrections. In particular, we conjecture that the critical two-point correlation g(r, L), with L the linear size, exhibits a two-length behavior: following the behavior $r^{2-d_c}$ governed by Gaussian fixed point at shorter distance and entering a plateau at larger distance whose height decays as $L^{-d_c/2}({\rm ln}L)^{\hat{p}}$ with $\hat{p}=1/2$ a logarithmic correction exponent. Using extensive Monte Carlo simulations, we provide complementary evidence for the predictions through the finite-size scaling of observables including the two-point correlation, the magnetic fluctuations at zero and non-zero Fourier modes, and the Binder cumulant. Our work sheds light on the formulation of logarithmic finite-size scaling and has practical applications in experimental systems.

scholarly journals Higgs-Yukawa model on the lattice

2018 ◽  
Vol 175 ◽  
pp. 08017 ◽  
Author(s):  
David Y.-J. Chu ◽  
Karl Jansen ◽  
Bastian Knippschild ◽  
C.-J. David Lin
Keyword(s):  
Fixed Point ◽  
Numerical Study ◽  
Finite Size ◽  
Finite Size Scaling ◽  
Yukawa Model ◽  
First Order ◽  
Thermal Phase ◽  
Analytical Formulae ◽  
Thermal Phase Transitions ◽  
Scalar Sector

We present results from two projects on lattice calculations for the Higgs-Yukawa model. First we report progress on the search of first-order thermal phase transitions in the presence of a dimension-six operator, with the choices of bare couplings that lead to viable phenomenological predictions. In this project the simulations are performed using overlap fermions. Secondly, our study for applying finite-size scaling techniques near the Gaussian fixed point of the Higgs-Yukawa model is presented. We discuss the analytical formulae for the Higgs Yukawa model and show results for a first numerical study in the pure O(4) scalar sector of the theory.

scholarly journals A NEW APPROACH TO DYNAMIC FINITE-SIZE SCALING

2003 ◽  
Vol 14 (07) ◽  
pp. 945-954 ◽  
Author(s):  
MEHMET DİLAVER ◽  
SEMRA GÜNDÜÇ ◽  
MERAL AYDIN ◽  
YİĞİT GÜNDÜÇ
Keyword(s):  
Three Dimensional ◽  
Finite Size ◽  
Taylor Series Expansion ◽  
Scaling Behavior ◽  
Dynamic Scaling ◽  
Finite Size Scaling ◽  
New Approach ◽  
Size Scaling ◽  
Dynamic Exponent ◽  
Good Agreement

In this work we have considered the Taylor series expansion of the dynamic scaling relation of the magnetization with respect to small initial magnetization values in order to study the dynamic scaling behavior of two- and three-dimensional Ising models. We have used the literature values of the critical exponents and of the new dynamic exponent x0 to observe the dynamic finite-size scaling behavior of the time evolution of the magnetization during early stages of the Monte Carlo simulation. For the three-dimensional Ising model we have also presented that this method opens the possibility of calculating z and x0 separately. Our results show good agreement with the literature values. Measurements done on lattices with different sizes seem to give very good scaling.

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