Matrix Product State Approach to the Finite-size Scaling Properties of the One-dimensional Critical Quantum Ising Model

박성빈,차민철 한국물리학회 2015 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.67 No.9

We investigate the finite-size scaling properties of the quantum phase transition in the onedimensional quantum Ising model with periodic boundary conditions by representing the ground state in matrix product state forms. The infinite time-evolving block decimation technique is used to optimize the states. A trace over a product of the matrices multiplied as many times as the number of sites yields the finite-size effects. For sufficiently large Schmidt ranks, the finite-size scaling behavior determines the critical point and the critical exponents whose values are consistent with the analytical results. We investigate the finite-size scaling properties of the quantum phase transition in the onedimensional quantum Ising model with periodic boundary conditions by representing the ground state in matrix product state forms. The infinite time-evolving block decimation techni que is used to optimize the states. A trace over a product of the matrices multiplied as many times as the number of sites yields the finite-size effects. For sufficiently large Schmidt ranks, the finite-size scaling behavior determines the critical point and the critical exponents whose values are consistent with the analytical results.

Role of Cutoff Scaling in Scale-Free Networks

하미순 한국물리학회 2018 New Physics: Sae Mulli Vol.68 No.5

We numerically study how the cutoff scaling of the upper degree affects the finite-size scaling (FSS) for physical models of scale-free networks (SFNs) in terms of the Ising model for annealed and quenched SFNs. Based on the hyperscaling argument and the results of S. H. Lee et al. [Phys. Rev. E 80, 051127 (2009)], we test the suggested FSS theory according to the value of the cutoff exponent, and find the cutoff of upper degree scales as a power law in the system size. In particular, we focus on finding the relevant length scale in finite SFNs near and at criticality. Moreover, we investigate the self-averaging property of the system in the presence of a quenched linking disorder as a way for exploring the fluctuations in the sampling disorder for the finite-degree sequence set.

Finite-size Scaling Properties of the One-dimensional Extended Bose-Hubbard Model

차민철,신종근 한국물리학회 2010 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.56 No.3

The critical properties of the one-dimensional hard-core extended Bose-Hubbard model at half-filling, involving both XY - and the Ising-symmetry breaking, are studied on a lattice up to 32 sites via the Lanczos method. The finite-size scaling behaviors as approached from either the insulator or the superfluid side are consistent with the presence of an essential singularity, suggesting that the transition has Kosterllitz-Thouless (KT)-type universal properties.

Dynamic Scaling Analysis of Critical Behaviors in Nonequilibrium Processes

하미순 한국물리학회 2014 새물리 Vol.64 No.8

We present a method for analyzing the critical behaviors systematically in nonequilibrium processes by using dynamic scaling, where we extend the well-known finite-size scaling (FSS) theory for the time evolution of major physical quantities that can indicate either a phase transition or some scaling property. Particularly, we discuss two cases: one is the one-dimensional (1D) thin film growth by vapor deposition polymerization (VDP), and the other is the synchronization of globally-coupled oscillators. Using a dynamic scaling analysis, we show that the universality issue of critical behaviors in nonequilibrium processes can be investigated even though the system is neither in the steady-state limit nor in the thermodynamic limit. Finally, in the context of this extended FSS analysis, we compare the VDP growth with the modified 1D Kardar Parisi-Zhang-type growth and classify the characteristics of synchronization transitions with various setups.

Critical Phenomena of the Generalized Epidemic Process

하미순 한국물리학회 2019 새물리 Vol.69 No.6

We investigate mixed-order critical phenomena of the generalized epidemic process (GEP) on random scale-free networks characterized by the power-law distribution pk k .The GEP is a minimal model of spreading behaviors. Near tricritical points (TCPs) derived by using the generating method, we numerically confirm the associated scaling exponents as functions of . In particular, we propose an extended finite-size scaling theory of the GEP and crossover scaling behaviors, which are also confirmed by using extensive Monte Carlo simulations. Our results show that near TCPs, the GEP is governed by two distinct length scales, whose nontrivial dependence on leads to rich transition behaviors.

Critical temperature of the Ising ferromagnet on the fcc, hcp, and dhcp lattices

North-Holland 2015 PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIO Vol.419 No.-

By an extensive Monte-Carlo calculation together with the finite-size-scaling and the multiple histogram method, the critical coupling constant (K<SUB>c</SUB>=J/k<SUB>B</SUB>T<SUB>c</SUB>) of the Ising ferromagnet on the fcc, hcp, and double hcp (dhcp) lattices were obtained with unprecedented precision: K<SUB>c</SUB><SUP>fcc</SUP>=0.1020707(2), K<SUB>c</SUB><SUP>hcp</SUP>=0.1020702(1), and K<SUB>c</SUB><SUP>dhcp</SUP>=0.1020706(2). The critical temperature T<SUB>c</SUB> of the hcp lattice is found to be higher than those of the fcc and the dhcp lattice. The dhcp lattice seems to have higher T<SUB>c</SUB> than the fcc lattice, but the difference is within error bars.

Critical Properties of the Three-dimensional XY Model in Large-scale Monte-Carlo Simulations

전인호,차민철,신종근 한국물리학회 2012 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.60 No.4

The critical properties of the three-dimensional XY model are studied in large-scale Monte-Carlo simulations by using a worm algorithm for the integer-current representation of the model. In large systems, singular behavior of the internal energy around the critical point is observed, and the finite-size scaling analyses of the superfluid stiffness lead us to find the critical inverse temperature <i>K_c</i> = 0.45416(1) and the correlation length critical exponent υ = 0.6708(5).

Stochastic Local Search in Random Constraint Satisfaction Problems

하미순 한국물리학회 2013 새물리 Vol.63 No.9

We present a method for studying the threshold behavior in random constraint satisfaction problems (CSPs) by using a stochastic local search (SLS), namely, a heuristic search. In particular, we employ the finite-size scaling concept of nonequilibrium absorbing phase transitions and address both the nature and the threshold of the solvable-unsolvable transition in terms of random K-satisfiability (K-SAT) problems, where K is the number of Boolean variables per logic clause. Based on the role of the noise parameter in the SLS, we find that the number of unsatisfied clauses (E) and the solving time (tsol) can reveal some valuable information about either the hidden structure of the solution space or the algorithmic complexity. As compared to two-value averaging over different samples, we show that survival-sample-averaged quantities in the steady-state limit are good and clear indicators of both the nature and the threshold of the phase transition in the thermodynamic limit.

Dynamic Phase Transition in Coupled Oscillators under a Periodic Symmetry-breaking Field

최중재,최무영,윤병국 한국물리학회 2010 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.57 No.6

We study numerically the dynamic responses of a system of globally coupled oscillators driven by periodic symmetry-breaking fields in the presence of noise. We find that the system undergoes a dynamic phase transition as the period or the amplitude of the symmetry-breaking field is varied at sufficiently low noise level. We employ a finite-size scaling analysis to investigate the characteristics of the dynamic transition. The obtained critical exponents turn out to be different from the mean-field values.

Generalized Conserved Lattice Gas on Random Networks

곽우섭,Sojeong PARK,하미순 한국물리학회 2016 New Physics: Sae Mulli Vol.66 No.10

We numerically investigate the mean-field (MF) behavior of the conserved lattice gas (CLG) model with effective temperature, where two types of random network topologies are considered, regular and random ones, and the effective temperature is controlled by using the thermal noise parameter. In particular, we focus on dynamic scaling for the spatiotemporal properties near the criticality of the CLG. Based on the MF theory and the finite-size scaling (FSS) analysis of continuous phase transitions, we present the MF values of the FSS exponent and the thermodynamic exponents. Finally, we conjecture a MF schematic phase diagram and discuss universality issues in the generalization of the CLG, which are compared with those in earlier results.