Research Summary

R1.

Low temperature properties of a random antiferromagnetic quantum spin chain.

Ma, Dasgupta and Hu developed an iterative algorithm to calculate properties of a quantum spin model with random nearest-neighbor couplings.
   1. S.-K. Ma, C. Dasgupta, and C.-K. Hu. Random antiferromagnetic Chain, Phys. Rev. Lett. 43, 1434-1437 (1979). PDF
           
R2.

Dynamic properties of a spin glass model.

Dasgupta, Ma, and Hu found that dynamic properties of a spin glass model at low temperatures can be understood from flipping of clusters with a distribution of barrier heights of the clusters.
  1. C. Dasgupta, S.-K. Ma, and C.-K. Hu. Dynamic properties of a spin glass model at low temperatures, Phys. Rev. B 20, 3837-3849 (1979). PDF
                
R3.

Percolation theory of phase transitions in Ising-type spin models and lattice hard-core particles.

Using subgraph expansion of Ising-type spin models in external fields, Hu found that thermal and magnetic properties of the spin models can be understood from the geometrical properties of the corresponding correlated percolation models. Using a Monte Carlo (MC) method, Hu and his student found that phase transitions of many hard-core particle models on two and three dimensional lattices are percolation transitions.
   1. C.-K. Hu. Percolation, clusters, and phase transitions in spin models, Phys. Rev. B 29, 5103-5108 (1984). PDF
   2. C.-K. Hu. Site-bond-correlated percolation and a sublattice-dilute Potts model at finite temperatures, Phys. Rev. B 29, 5109-5116 (1984). PDF
   3. C.-K. Hu. Bond-correlated percolation model and unusual behaviour of supercooled water, J. Phys. A: Math. Gen. 16, L321-326 (1983). PDF
    4. C.-K. Hu and K.-S. Mak. Percolation and phase transitions of hard-core particles on lattices: Monte-Carlo approach, Phys. Rev. B (Rapid Communications) 39, 2948-2951 (1989). PDF
    5. C.-K. Hu and K.-S. Mak. Percolation and phase transitions of hard-core particles on lattices with pair interactions, Phys. Rev. B 42, 965-968 (1990). PDF
          
R4.

Percolation renormalization group (RG) method for phase transition models.

Based on R3, Hu and his student (C.-N. Chen) developed percolation RG methods to calculate thermal and magnetic properties of phase transition models.
  1. C.-K. Hu and C.-N. Chen. Percolation renormalization group approach to the q-state Potts model. Phys. Rev. B 38, 2765-2778 (1988). PDF
  2. C.-K. Hu and C.-N. Chen . Percolation renormalization group calculations of equations of state for the Potts model, Phys. Rev. B 39, 4449-4452 (1989). PDF
  3. C.-K. Hu and C.-N. Chen. Percolation renormalization group approach to the hard square model, Phys. Rev. B 43, 6184-6185 (1991). PDF
  4. C.-N. Chen and C.-K. Hu. Fast algorithm to calculate exact geometrical factors for the q-state Potts model, Phys. Rev. B 43, 11519-11522(R) (1991). PDF
       
R5.

Histogram MC methods for percolation and spin models.

Based on R4, Hu proposed a histogram MC (HMC) simulation method and a HMC renormalization group method that can efficiently use MC data for calculating accurate global and critical quantities of percolation and spin models.
  1. C.-K. Hu. Histogram Monte Carlo renormalization group method for percolation problems, Phys. Rev. B1 46, 6592-6595 (1992). PDF
  2. C.-K. Hu. Histogram Monte Carlo renormalization group method for phase transition models without critical slowing down, Phys. Rev. Lett. 69, 2739-2742 (1992). PDF
  3. J.-A. Chen and C.-K. Hu. Histogram important sampling Monte Carlo method for the q-state Potts model, Phys. Rev. B 50, 6260-6263 (1994). PDF
                 
R6.

Anomalous transport in dynamical systems.

Wang and Hu obtained rigorous results for dynamical systems which show anomalous diffusion.
 

1.

 X.-J. Wang and C.-K. Hu. Anomalous transport in dynamical systems: a rigorous theory of all orders, Phys. Rev. E 48, 728-733 (1993). PDF
                 
R7.

Universal finite-size scaling functions (UFSSFs) and exponents for percolation and Ising models.

Using R5 and other MC methods, Hu and collaborators found UFSSFs for a variety of percolation models, and UFSSFs and a universal dynamic critical exponent for the Ising model.
  1. C.-K. Hu, C.-Y. Lin, and J.-A. Chen. Universal scaling functions in critical phenomena, Phys. Rev. Lett. 75, 193-196  PDF   and 2786(E) (1995). PDF
  2. C.-K. Hu and C.-Y. Lin. Universal scaling functions for numbers of percolating clusters on planar lattices, Phys. Rev. Lett. 77, 8-11 (1996). PDF
  3. F.-G. Wang and C.-K. Hu. Universality in dynamic critical phenomena, Phys. Rev. E 56, 2310-2313 (1997). PDF
  4. C.-Y. Lin and C.-K. Hu. Universal finite-size scaling functions for percolation on three-dimensional lattices, Phys. Rev. E 58, 1521-1527 (1998). PDF
  5. Y. Okabe, K. Kaneda, M. Kikuchi, and C.-K. Hu. Universal finite-size scaling functions for critical systems with tilt boundary conditions, Phys. Rev. E. 59, 1585-1588 (1999). PDF
  6. Y. Tomita, Y. Okabe, and C.-K. Hu. Cluster analysis and finite-size scaling for Ising spin systems, Phys. Rev. E 60, 2716-2720 (1999). PDF
  7. H.-P. Hsu, S.-C. Lin, and C.-K. Hu. Universal scaling functions for bond percolation on planar random and square lattices with multiple percolating clusters, Phys. Rev. E 64, 016127 (2001). PDF
                 
R8.

Partition function zeroes of the Potts model.

Chen, Hu, and Wu proposed a distribution of partition function zeroes (Fisher zeros) of the Potts model, which has inspired much interest in this topic in recent years.
 

1.

 C.-N. Chen, C.-K. Hu, and F. Y. Wu. Partition function zeroes of the square lattice Potts model, Phys. Rev. Lett. 76, 169-172 (1996). PDF
         
R9.

Universal amplitude ratios for spin models.

Considering the Ising model on Nx¥ square, triangle, and honeycomb lattices and a quantum spin model on a ring of N sites, Izmailian and Hu found universal amplitude ratios for these systems.
 

1.

 N. Sh. Izmailian and C.-K. Hu. Exact universal amplitude ratios for two-dimensional Ising models and a quantum spin chain, Phys. Rev. Lett. 86 , 5160-5163 (2001). PDF
         
R10.

Exact finite-size corrections and UFSSFs for the Ising model.

Hu and collaborators obtained exact finite-size corrections for thermodynamic quantities of the Ising model and used such results to obtain UFSSFs for the Ising model with exact non-universal metric factors.
  1. N. Sh. Izmailian and C.-K. Hu. Exact amplitude ratio and finite-size corrections for the MxN square lattice Ising model, Phys. Rev. E 65, 036103 (2002). PDF
  2. N. Sh. Izmailian, K. B Oganesyan and C.-K. Hu. Exact finite-size corrections for the square lattice Ising model with Brascamp-Kunz boundary conditions, Phys. Rev. E 65, 056132 (2002). PDF
  3. M.-C. Wu, C.-K. Hu and N.Sh. Izmailian. Universal finite-size scaling function with exact nonuniversal metric factors, cond-mat/0303166 and Phys. Rev. E 67, 065103 (R) (2003). PDF
  4. E. V. Ivashkevich, N.Sh. Izmailian, and C.-K. Hu. Kronecker's double series and exact asymptotic expansions for free models of statistical mechanics on torus, J. Phys. A: Math. and Gen. 35, 5543-5561 (2002). PDF
        
R11.

Critical behavior of sandpile and avalanche models.

Hu and collaborators found universal critical behavior for toppling waves of a planar sandpile model and an asymmetric avalanche model on a ring.
  1. C.-K. Hu, E. V. Ivashkevich, C.-Y. Lin, and V. B. Priezzhev. Inversion symmetry and exact critical exponents of dissipating waves in the sandpile model, Phys. Rev. Lett. 85, 4048-4051 (2000). PDF
  2. C.-K. Hu and C.-Y. Lin. Universality in critical exponents for toppling waves of the BTW sandpile model on two-dimensional lattices, Physica A, 318, 92-100 (2003). PDF
  3. V.B. Priezzhev, E.V. Ivashkevich, A.M. Povolotsky, and C.-K. Hu. Exact phase diagram for an asymmetric avalanche process, Phys. Rev. Lett. 87, 084301 (2001). PDF
  4. A.M. Povolotsky, V.B. Priezzhev, and C.-K. Hu. The asymmetric avalanche process, J. Stat. Phys. 111, 1149-1182 (2003). PDF
  5. A.M. Povolotsky, V.B. Priezzhev, and C.-K. Hu. Transition from Kardar-Parizi-Zhang to tilted interface critical behavior in a solvable asymmetric avalanche model, Phys. Rev. Lett. 91, 255701 (2003). PDF
          
R12.

Computing package and algorithms for simulations of proteins in parallel computers.

Hu and collaborators developed computing package and algorithms for calculating structures and properties of proteins in parallel computers.
   1. F. Eisenmenger, U. H.E. Hansmann, S. Hayryan, and C.-K. Hu. [SMMP] A modern package for simulation of proteins, Computer Phys. Commu., 138, 192-212 (2001). PDF
   2. S. Hayrian, C.-K. Hu, S.-Y. Hu and R.-J. Shang. Multicanonical parallel simulation of proteins with continuous potentials, J. Comp. Chem. 22, 1287-1296 (2001). PDF
   3. C.-Y. Lin, C.-K. Hu, and U. H.E. Hansmann. Parallel tempering simulations of HP-36, Proteins -- Structure, Function and Genetics 52, 436-445 (2003). PDF