scholarly journals Critical behavior of the two-dimensional Ising model in a transverse field: A density-matrix renormalization calculation

1998 ◽  
Vol 57 (14) ◽  
pp. 8494-8500 ◽  
Author(s):  
M. S. L. du Croo de Jongh ◽  
J. M. J. van Leeuwen
Keyword(s):  
Ising Model ◽  
Density Matrix ◽  
Critical Behavior ◽  
Transverse Field ◽  
Two Dimensional ◽  
Density Matrix Renormalization

scholarly journals ANALYTIC FORMULATIONS OF THE DENSITY MATRIX RENORMALIZATION GROUP

1996 ◽  
Vol 11 (17) ◽  
pp. 3145-3174 ◽  
Author(s):  
MIGUEL A. MARTÍN-DELGADO ◽  
GERMÁN SIERRA
Keyword(s):  
Renormalization Group ◽  
Ising Model ◽  
Density Matrix ◽  
Transverse Field ◽  
Density Matrix Renormalization Group ◽  
Critical Properties ◽  
Density Matrix Renormalization ◽  
Lattice Size ◽  
Target States ◽  
Block Renormalization Group

We present two new analytic formulations of the density matrix renormalization group (DMRG) method. In these formulations we combine the block renormalization group (BRG) procedure with the variational and Fokker-Planck methods. The BRG method is used to reduce the lattice size while the latter are used to construct approximate target states to compute the block density matrix. We apply our DMRG methods to the Ising model in a transverse field (ITF model) and compute several of its critical properties, which are then compared with the old BRG results.

scholarly journals Pseudo-Yang-Lee Edge Singularity Critical Behavior in a Non-Hermitian Ising Model

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 780
Author(s):  
Liang-Jun Zhai ◽  
Guang-Yao Huang ◽  
Huai-Yu Wang
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Critical Behavior ◽  
Critical Region ◽  
Numerical Study ◽  
Transverse Field ◽  
Scaling Theory ◽  
New Order ◽  
Edge Singularity ◽  
Transverse Field Ising Model

The quantum phase transition of a one-dimensional transverse field Ising model in an imaginary longitudinal field is studied. A new order parameter M is introduced to describe the critical behaviors in the Yang-Lee edge singularity (YLES). The M does not diverge at the YLES point, a behavior different from other usual parameters. We term this unusual critical behavior around YLES as the pseudo-YLES. To investigate the static and driven dynamics of M, the (1+1) dimensional ferromagnetic-paramagnetic phase transition ((1+1) D FPPT) critical region, (0+1) D YLES critical region and the (1+1) D YLES critical region of the model are selected. Our numerical study shows that the (1+1) D FPPT scaling theory, the (0+1) D YLES scaling theory and (1+1) D YLES scaling theory are applicable to describe the critical behaviors of M, demonstrating that M could be a good indicator to detect the phase transition around YLES. Since M has finite value around YLES, it is expected that M could be quantitatively measured in experiments.

Effects of Superaging and Percolation Crossover on the Nonequilibrium Critical Behavior of the Two-Dimensional Disordered Ising Model

JETP Letters ◽  
2018 ◽  
Vol 107 (9) ◽  
pp. 569-576 ◽  
Author(s):  
V. V. Prudnikov ◽  
P. V. Prudnikov ◽  
E. A. Pospelov ◽  
P. N. Malyarenko
Keyword(s):  
Ising Model ◽  
Critical Behavior ◽  
Two Dimensional
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