Chi-Ning Chen

Heat capacity decomposition by partition function zeros for interacting self-avoiding walks

A novel method based on partition function zeros is developed to demonstrate the additional advantages by considering both loci of partition function zeros and thermodynamical functions associated with them. With this method, the first pair of complex conjugate zeros (first zeros) can be defined without ambiguity and the critical point of a small system can be defined as the peak position of the heat capacity component associated with the first zeros. For the system with two phase transitions, two pairs of first zeros corresponding to two phase transitions can be identified and two overlapping phase transitions can be well separated. This method is applied to the interacting self-avoiding walk (ISAW) of homopolymer with N monomers on the simple cubic lattice, which has a collapse transition at a higher temperature and a freezing transition at a low temperature. The exact partition functions ZN with N up to 27 are calculated and our approach gives a clear scenario for the collapse and the freezing transitions.

Crossover behavior of stock returns and mean square displacements of particles governed by the Langevin equation

It is found that the mean square log-returns calculated from the high-frequency one-day moving average of US and Taiwan stocks with the time internal τ show ballistic behavior with the exponent for small τ and show diffusion-like behavior with the exponent for large τ. Such a crossover behavior can be well described by the mean square displacements of particles governed by the Langevin equation of motion. Thus, θ and D can be considered, respectively, as the temperature-like and diffusivity-like kinetic parameters of the market, and they can be used to characterize the behavior of the market.

Partition function zeros of the Q-state Potts model for non-integer Q

The distribution of the zeros of the partition function in the complex temperature plane (Fisher zeros) of the two-dimensional Q-state Potts model is studied for non-integer Q. On L×L self-dual lattices studied (L⩽8), no Fisher zero lies on the unit circle p0=eiθ in the complex p=(eβJ−1)/Q plane for Q 1 and the number of such zeros increases with increasing Q. The ferromagnetic and antiferromagnetic properties of the Potts model are investigated using the distribution of the Fisher zeros. For the Potts ferromagnet we verify the den Nijs formula for the thermal exponent yt. For the Potts antiferromagnet we also verify the Baxter conjecture for the critical temperature and present new results for the thermal exponents in the range 0

Efficient algorithm for computing exact partition functions of lattice polymer models

Abstract Polymers are important macromolecules in many physical, chemical, biological and industrial problems. Studies on simple lattice polymer models are very helpful for understanding behaviors of polymers. We develop an efficient algorithm for computing exact partition functions of lattice polymer models, and we use this algorithm and personal computers to obtain exact partition functions of the interacting self-avoiding walks with N monomers on the simple cubic lattice up to N = 28 and on the square lattice up to N = 40 . Our algorithm can be extended to study other lattice polymer models, such as the HP model for protein folding and the charged HP model for protein aggregation. It also provides references for checking accuracy of numerical partition functions obtained by simulations.

X-ray radiation from a relativistic charge in superconducting granule device by diffusional scattering of pseudophotons

A recent experiment was carried out to test a new type of X-ray detector. It consists of superconducting microspheres mixed randomly in dielectric material. X-ray radiation is generated from a relativistic charged particles passing through the detector. The number of X-ray photons detected depends on the particle energy, γ=E/mc2, almost linearly in the energy range from 1 to 10 GeV. We explain this energy dependence by diffusional scattering of pseudophotons. This shows a closer agreement with the experimental result than the description from the conventional transition radiation theory.

Percolation renormalisation and simulation studies of the potts model

Abstract Based on the connection between the q-state Potts model (QPM) and the q-state bond-correlated percolation (QBCPM), Hu proposed a percolation renormalisation group method (PRGM) and Swendsen and Wang proposed a percolation Monte-Carlo simulation method (PMCSM) for studying properties of the QPM. The PRGM gives the exact free energy and the critical exponent for the one-dimensional QPM and the accurate free energy and critical physical quantities for the suare lattice QPM. The PMCSM and multiple labeling technique are applied to calculate the percolation probability, the mean cluster-size, the average number of occupied bonds, and the fluctuations of the number of bonds for the QBCPM on the square and simple cubic lattices. From such results, we obtain accurate phase transition points for the QPM.