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Random deposition model with surface relaxation in higher dimensions
Kwak, Wooseop,Kim, Jin Min Elsevier Science B.V., Amsterdam. 2019 PHYSICA A Vol.520 No.-
<P><B>Abstract</B></P> <P>A random deposition model with surface relaxation, so-called the Family model is studied in higher dimensions. In three dimensions, the surface width W ( t ) characterizing the roughness of a surface grows as 2 b log t at the beginning and becomes saturated at 2 a log L for t ≫ <SUP> L z </SUP> , where L is the system size. The dynamic exponent z = 1 . 99 ( 2 ) is estimated from the relation z = a ∕ b and a nice data collapse of the scaling plot <SUP> W 2 </SUP> ( L , t ) ∼ log <SUP> L 2 a </SUP> g t ∕ <SUP> L z </SUP> is given with z = 2 . In four dimensions, the surface width approaches an intrinsic width <SUB> W int </SUB> with a small correction term <SUP> W 2 </SUP> ( L , t ) = W int 2 − <SUP> L 2 α </SUP> f t ∕ <SUP> L z </SUP> , where z ≈ 1 . 97 and negative exponent α ≈ − 0 . 52 are obtained. Our results support that the Family model belongs to the Edwards–Wilkinson universality class even in higher dimensions.</P> <P><B>Highlights</B></P> <P> <UL> <LI> The random deposition model with surface diffusion, the Family model, is studied. </LI> <LI> We measure critical exponents by using calculating the surface width. </LI> <LI> In three dimensions, the Family model shows the logarithmic growth. </LI> <LI> In four dimensions, we measure negative values of critical exponents. </LI> <LI> The Family model corresponds to the Edwards–Wilkinson equation below four dimensions. </LI> </UL> </P>
김승연,Wooseop Kwak 한국물리학회 2014 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.65 No.4
The critical temperature and the thermal scaling exponent of the square-lattice Blume-Capelmodel are obtained as functions of fugacity by calculating the partition function zeros in the complextemperature plane of the square-lattice Blume-Capel antiferromagnet for the first time. The thermalscaling exponent yt determines the specific-heat critical exponent and the correlation-length criticalexponent. The value of yt = 2 indicates a strong first-order phase transition in two dimensionswhereas yt = 1 corresponds to an Ising-class second-order phase transition. The full spectrum(from yt = 2 to yt = 1) of the thermal scaling exponent for the square-lattice Blume-Capel model isevaluated for the first time. The phase diagram of the square-lattice Blume-Capel model, includingthe tricritical point, is also obtained, and it is compared with other results in the literature.
Does the Majority Voter Model Belong to the Ising Universality Class on Three Dimensions?
Jae-Suk Yang,Wooseop Kwak,김인묵 한국물리학회 2008 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.52 No.6
We study the critical properties of the majority voter model on three dimensions. The majority voter model belongs to the Ising universality class on two dimensions, but does not on three dimensions. We have modified the majority voter model by considering the difference between the local and the global configuration energies. This modified majority voter model is found to belong to the same universality class as that of the Ising model on three dimensions. We study the critical properties of the majority voter model on three dimensions. The majority voter model belongs to the Ising universality class on two dimensions, but does not on three dimensions. We have modified the majority voter model by considering the difference between the local and the global configuration energies. This modified majority voter model is found to belong to the same universality class as that of the Ising model on three dimensions.
Asymmetric field dependence of the specific heat of the three-state Potts model on a square lattice
Kim Seung-Yeon,Kwak Wooseop 한국물리학회 2021 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.79 No.12
Even in zero magnetic field, the exact solution of the three-state Potts model on a square lattice has never been obtained. Also, the properties of the three-state Potts model on a square lattice are little known for nonzero magnetic field. Unlike the Ising model which follows the Lee–Yang circle theorem and is symmetric under an external magnetic field, the three-state Potts model violates the circle theorem, and its properties in an external magnetic field are asymmetric for positive and negative external magnetic fields. The Wang–Landau sampling method is applied to estimate the unknown density of states g(ε, μ) as a function of the microscopic energy ε and the microscopic magnetization μ for the three-state Potts model on a square lattice in an external magnetic field. Based on the estimated density of states, the properties of the asymmetric field dependence of the specific heat for the three-state Potts model on a square lattice are studied in an external magnetic field.
Specific-Heat Anomaly of the Kagomé-Lattice Ising Model in a Magnetic Field
Kim Seung-Yeon,Kwak Wooseop 한국물리학회 2020 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.77 No.8
The properties of the kagomé-lattice Ising model in an external magnetic field B have not been known well. The specific-heat anomaly of the kagomé-lattice Ising model in an external magnetic field is investigated based on the enthalpy fluctuation. As the magnetic field increases, the specific heat maximum decreases, but it approaches non-zero value for large magnetic field. In particular, the asymptotic line to the specific-heat maximum temperature Th(B) follows Th(B) = 0.8335565596 (B + 4). The well-known experimentalist formula Tp(B) = 0.8335565596 B for paramagnet shows the same slope as the asymptotic line Th(B) of the kagomé-lattice Ising model in an external magnetic field.