| 1. |
- Baek, Seung Ki, 1979-, et al.
(författare)
-
Comment on `Six-state clock model on the square lattice: Fisher zeroapproach with Wang-Landau sampling'
- 2010
-
Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. - 1063-651X .- 1095-3787. ; 81:6, s. 3101-
-
Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- Hwang in [Phys. Rev. E {\bf{80}}, 042103 (2009)] suggested that the two transitions of the six-state clock model on the square lattice are\emph{not} of the Kosterlitz-Thouless type. Here we show from simulations thatat the upper transition, the helicity modulus does make a discontinuous jumpto zero. This gives strong evidence for a Kosterlitz-Thoulesstransition.
|
|
| 2. |
- Baek, Seung Ki, et al.
(författare)
-
Critical condition of the water-retention model
- 2012
-
Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. - : American Physical Society. - 1539-3755 .- 1550-2376. ; 85:3, s. 032103-
-
Tidskriftsartikel (refereegranskat)abstract
- We study how much water can be retained without leaking through boundarieswhen each unit square of a two-dimensional lattice is randomly assigned a blockof unit bottom area but with different heights from zero to $n-1$.As more blocks are put into the system,there exists a phase transition beyond whichthe system retains a macroscopic volume of water.We locate the critical points and verify that the criticalitybelongs to the two-dimensional percolation universality class.If the height distribution can be approximated as continuous for large $n$,the system is always close to a critical point and the fraction of the areabelow the resulting water level is given by the percolation threshold.This provides a universal upper bound ofareas that can be covered by water in a random landscape.
|
|
| 3. |
- Baek, Seung Ki, et al.
(författare)
-
Critical temperatures of the three- and four-state Potts models on the kagome lattice
- 2011
-
Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. - : American Physical Society. - 1063-651X .- 1095-3787. ; 83:6, s. 061104-
-
Tidskriftsartikel (refereegranskat)abstract
- The value of the internal energy per spin is independent of the strip widthfor a certain class of spin systems on two dimensional infinite strips. Itis verified that the Ising model on the kagome lattice belongs to this classthrough an exact transfer-matrix calculation of the internal energy for thetwo smallest widths. More generally, one can suggest an upper bound forthe critical coupling strength $K_c(q)$ for the $q$-state Potts model fromexact calculations of the internal energy for the two smallest stripwidths. Combining this with the corresponding calculation for the duallattice and using an exact duality relation enables us to conjecture thecritical coupling strengths for the three- and four-state Pottsmodels on the kagome lattice. The values are $K_c(q=3)=1.056~509~426~929~0$and $K_c(q=4) = 1.149~360~587~229~2$,and the values can, in principle, be obtained to an arbitrary precision. Wediscuss the fact that these values are in the middle of earlierapproximate results and furthermore differ from earlier conjecturesfor the exact values.
|
|
| 4. |
- Baek, Seung Ki, et al.
(författare)
-
Dworkin's Paradox
- 2012
-
Ingår i: PLOS ONE. - : Public Library of Science (PLoS). - 1932-6203. ; 7:6, s. e38529-
-
Tidskriftsartikel (refereegranskat)abstract
- How to distribute welfare in a society is a key issue in the subject of distributional justice, which is deeply involved with notions of fairness. Following a thought experiment by Dworkin, this work considers a society of individuals with different preferences on the welfare distribution and an official to mediate the coordination among them. Based on a simple assumption that an individual's welfare is proportional to how her preference is fulfilled by the actual distribution, we show that an egalitarian preference is a strict Nash equilibrium and can be favorable even in certain inhomogeneous situations. These suggest how communication can encourage and secure a notion of fairness.
|
|
| 5. |
- Baek, Seung Ki, et al.
(författare)
-
Ising model on a hyperbolic plane with a boundary
- 2011
-
Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. - : American Physical Society. - 1539-3755 .- 1550-2376. ; 84, s. 032103-
-
Tidskriftsartikel (refereegranskat)abstract
- A hyperbolic plane can be modeled by a structure called the enhanced binarytree. We study the ferromagnetic Ising model on top of the enhanced binarytree using the renormalization-group analysis in combination withtransfer-matrix calculations. We find a reasonable agreement with MonteCarlo calculations on the transition point, and the resulting criticalexponents suggest the mean-field surface critical behavior.
|
|
| 6. |
- Baek, Seung Ki, et al.
(författare)
-
Kosterlitz-Thouless transition of magnetic dipoles on thetwo-dimensional plane
- 2011
-
Ingår i: Physical Review B. Condensed Matter and Materials Physics. - : APS. - 1098-0121 .- 1550-235X. ; 83:18, s. 184409-5 p
-
Tidskriftsartikel (refereegranskat)abstract
- The universality class of a phase transition is often determined by factorslike dimensionality and inherent symmetry. We study the magneticdipole system in which the ground-state symmetry and the underlying latticestructure are coupled to each other in an intricate way. A two-dimensional(2D)square-lattice system of magnetic dipoles undergoes an order-disorder phasetransition belonging to the 2D Ising universality class.According to Prakash and Henley [Phys. Rev. B {\bf 42}, 6572 (1990)], this can berelated to the fourfold-symmetric ground states which suggests a similarityto the four-state clock model. Provided that this type ofsymmetry connection holds true, the magnetic dipoles on a honeycomb lattice,which possess sixfold-symmetric ground states, should exhibit aKosterlitz-Thouless transition in accordance with the six-state clock model.This is verified through numerical simulations in the present investigation.However, it is pointed out that this symmetry argument does not alwaysapply, which suggests that factors other than symmetry can be decisive forthe universality class of the magnetic dipole system.
|
|
| 7. |
- Baek, Seung Ki, 1979-, et al.
(författare)
-
Numerical Study of Game Theory
- 2010
-
Ingår i: New Physics. - Seoul : The Korean Physical Society. - 0374-4914. ; 60:9, s. 943-951
-
Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- Game-theoretic approach has been providing a powerful tool in qualitative understanding of macroscopic social phenomena in social sciences, e.g., in economics and political science. Recently, researchers in physics, especially in statistical physics, use these game-theoretic approaches but in more quantitative way and have been producing a variety of interesting results in the new research area called ’sociophysics’ by studying human society as a complex system. This work introduces recent works that have tackled combinatorial complexities arising in game-theoretic studies with the aid of simplified assumptions and numerical computations. We first show how cooperation emerges in the prisoner’s dilemma game when each player’s memory capacity is enhanced and suggest that the intelligent tit-for-tat strategy plays a crucial role in the history of cooperation. And then it is numerically shown that there is a certain case of simultaneous coordination among many players where the system has a high risk of failure when everyone is willing to follow the coordination, which is actually higher than when some are not concerned about it. Lastly, we discuss mathematical treatment of an equilibrium solution for a reverse auction game, which is a variant of the minority game, and its computational approach.
|
|
| 8. |
- Baek, Seung Ki, et al.
(författare)
-
Quantum Monte Carlo study of the transverse-field quantum Ising modelon infinite-dimensional structures
- 2011
-
Ingår i: Physical Review B Condensed Matter. - : American Physical Society. - 0163-1829 .- 1095-3795. ; 84, s. 174419-
-
Tidskriftsartikel (refereegranskat)abstract
- In a number of classical statistical-physical models, there exists acharacteristic dimensionality called the upper critical dimension abovewhich one observes the mean-field critical behavior. Instead of constructinghigh-dimensional lattices, however, one can also considerinfinite-dimensional structures, and the question is whether this mean-fieldcharacter extends to quantum-mechanical cases as well. We thereforeinvestigate the transverse-field quantum Ising model on the globally couplednetwork and on the Watts-Strogatz small-world network by means of quantum MonteCarlo simulations and the finite-size scaling analysis. We confirm that bothof the structures exhibit critical behavior consistent with the mean-fielddescription. In particular, we show that the existing cumulant methodhas difficulty in estimating the correct dynamic critical exponent andsuggest that an order parameter based on the quantum-mechanicalexpectation value can be a practically useful numerical observable todetermine critical behavior when there is no well-defined dimensionality.
|
|
| 9. |
- Baek, Seung Ki, et al.
(författare)
-
Residual discrete symmetry of the five-state clock model
- 2013
-
Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. - 1539-3755 .- 1550-2376. ; 88:1
-
Tidskriftsartikel (refereegranskat)abstract
- It is well known that the q-state clock model can exhibit a Kosterlitz-Thouless (KT) transition if q is equal to or greater than a certain threshold, which has been believed to be five. However, recent numerical studies indicate that helicity modulus does not vanish in the high-temperature phase of the five-state clock model as predicted by the KT scenario. By performing Monte Carlo calculations under the fluctuating twist boundary condition, we show that it is because the five-state clock model does not have the fully continuous U(1) symmetry even in the high-temperature phase while the six-state clock model does. We suggest that the upper transition of the five-state clock model is actually a weaker cousin of the KT transition so that it is q≥6 that exhibits the genuine KT behavior
|
|
| 10. |
- Baek, Seung Ki, 1979-, et al.
(författare)
-
Surface and bulk criticality in midpoint percolation
- 2010
-
Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. - 1063-651X .- 1095-3787. ; 81:4, s. 1108-6 sidor
-
Tidskriftsartikel (refereegranskat)abstract
- The concept of midpoint percolation has recently been applied tocharacterize the double percolation transitions in negatively curvedstructures. Regular $d$-dimensional hypercubic lattices are in the presentwork investigated using the same concept.Specifically, the site-percolation transitions at the critical thresholds areinvestigated for dimensions up to $d=10$ by means of the Leath algorithm.It is shown that the explicit inclusion of the boundariesprovides a straightforward way to obtain critical indices, both for thebulk and surface parts. At and above the critical dimension $d=6$, it isfound that the percolation cluster contains only a finite number of surfacepoints in the infinite-size limit. This is in accordance with theexpectation from studies of lattices with negative curvature. It is alsofound that the number of surface points, reached by the percolation clusterin the infinite limit, approaches $2d$ for large dimensions $d$. We alsonote that the size dependence in proliferation of percolatingclusters for $d\ge 7$ can be obtained by solely counting surface pointsof the midpoint cluster.
|
|
