arXiv subjects

Yuzhi Liu

Publications and source records attributed to Yuzhi Liu.

59 records · Page 4Linked to original sources

arXiv2010

Fisher's zeros as boundary of renormalization group flows in complex coupling spaces

We propose new methods to extend the renormalization group transformation to complex coupling spaces. We argue that the Fisher's zeros are located at the boundary of the complex basin of attraction of infra-red fixed points. We support this picture with numerical calculations at finite volume for two-dimensional O(N) models in the large-N limit and the hierarchical Ising model. We present numerical evidence that, as the volume increases, the Fisher's zeros of 4-dimensional pure gauge SU(2) lattice gauge theory with a Wilson action, stabilize at a distance larger than 0.15 from the real axis in the complex beta=4/g^2 plane. We discuss the implications for proofs of confinement and searches for nontrivial infra-red fixed points in models beyond the standard model.

hep-lat↗

arXiv2009

Finite Size Scaling and Universality in SU(2) at Finite Temperature

We study the 4-th Binder cumulant on $4\times{N_σ}^3$ lattices for a pure SU(2) gauge theory. We use 20 data points for a sequence of ${N_σ}$ in $β$ intervals shrinking when ${N_σ}$ increases, in order to reduce the nonlinear effects. Using a log-log fit of the slope versus ${N_σ}$, we obtain the preliminary result $ν=0.637(11)$ in reasonably good agreement with the value for the 3D Ising model universality class. The corrections due to irrelevant directions appear to be dominated by a term proportional to ${N_σ}^{-2.03(4)}$ which seems compatible with the breaking of rotational symmetry.

hep-lat↗

arXiv2008

Approximate forms of the density of states

We compare MC calculations of the density of states in SU(2) pure gauge theory with the weak and strong coupling expansions. Surprisingly, the range of validity of the two approximations overlap significantly, however the large order behavior of both expansions appear to be similar to the corresponding expansions of the plaquette. We discuss the implications for the calculation of the Fisher's zeros of the partition function.

hep-lat↗

arXiv2008

Volume dependence of Fisher's zeros

We study the location of the partition function zeros in the complex beta plane (Fisher's Zeros) for SU(2) lattice gauge theory on L^4 lattices. We discuss recent attempts to locate complex zeros for L=4 and 6. We compare results obtained using various polynomial approximations of the logarithm of the density of states and a straightforward MC reweighting. We conclude that the method based on a combination of discrete Chebyshev orthogonality and patching plaquette distributions at different beta provides the more reliable estimates.

hep-lat↗

arXiv2008

Series expansions of the density of states in SU(2) lattice gauge theory

We calculate numerically the density of states n(S) for SU(2) lattice gauge theory on $L^4$ lattices. Small volume dependence are resolved for small values of S. We compare $ln(n(S))$ with weak and strong coupling expansions. Intermediate order expansions show a good overlap for values of S corresponding to the crossover. We relate the convergence of these expansions to those of the average plaquette. We show that when known logarithmic singularities are subtracted from $ln(n(S))$, expansions in Legendre polynomials appear to converge and could be suitable to determine the Fisher's zeros of the partition function.

hep-lat↗