arXiv subjects

Wen-Jer Tzeng

Publications and source records attributed to Wen-Jer Tzeng.

5 recordsLinked to original sources

arXiv2010

Exact Solution of a Monomer-Dimer Problem: A Single Boundary Monomer on a Non-Bipartite Lattice

We solve the monomer-dimer problem on a non-bipartite lattice, the simple quartic lattice with cylindrical boundary conditions, with a single monomer residing on the boundary. Due to the non-bipartite nature of the lattice, the well-known method of a Temperley bijection of solving single-monomer problems cannot be used. In this paper we derive the solution by mapping the problem onto one on close-packed dimers on a related lattice. Finite-size analysis of the solution is carried out. We find from asymptotic expansions of the free energy that the central charge in the logarithmic conformal field theory assumes the value $c=-2$.

cond-mat.stat-mech↗

arXiv2006

Scaling Analysis and Systematic Extraction of Macroscopic Structures in Fluctuating Systems of Arbitrary Dimensions

Many fluctuating systems consist of macroscopic structures in addition to noisy signals. Thus, for this class of fluctuating systems, the scaling behaviors are very complicated. Such phenomena are quite commonly observed in Nature, ranging from physics, chemistry, geophysics, even to molecular biology and physiology. In this paper, we take an extensive analytical study on the ``generalized detrended fluctuation analysis'' method. For continuous fluctuating systems in arbitrary dimensions, we not only derive the explicit and exact expression of macroscopic structures, but also obtain the exact relations between the detrended variance functions and the correlation function. Besides, we undertake a general scaling analysis, applicable for this class of fluctuating systems in any dimensions. Finally, as an application, we discuss some important examples in interfacial superroughening phenomena.

cond-mat.stat-mech↗

arXiv1996

Exact Solution of Frenkel-Kontorova Models with a Complete Devil's Staircase in Higher Dimensions

We solve exactly a class of Frenkel-Kontorova models with piecewise parabolic potential, which has $d$ sub-wells in a period. With careful analysis, we show that the phase diagram of the minimum enthalpy configurations exhibits the structure of a complete $d$-dimensional devil's staircase. The winding number of a minimum enthalpy configuration is locked to rational values, while the fraction of atoms in each sub-well is locked to values which are sub-commensurable with the winding number.

solv-int↗

arXiv1996

Farey Tree and the Frenkel-Kontorova Model

We solved the Frenkel-Kontorova model with the potential $V(u)= -\frac{1}{2} |λ|(u-{\rm Int}[u]-\frac{1}{2})^2$ exactly. For given $|λ|$, there exists a positive integer $q_c$ such that for almost all values of the tensile force $σ$, the winding number $ω$ of the ground state configuration is a rational number in the $q_c$-th level Farey tree. For fixed $ω=p/q$, there is a critical $λ_c$ when a first order phase transition occurs. This phase transition can be understood as the dissociation of a large molecule into two smaller ones in a manner dictated by the Farey tree. A kind of ``commensurate-incommensurate'' transition occurs at critical values of $σ$ when two sizes of molecules co-exist. ``Soliton'' in the usual sense does not exist but induces a transformation of one size of molecules into the other.

solv-int↗

arXiv1995

Exact Solution of an One Dimensional Deterministic Sandpile Model

Using the transfer matrix method, we give the exact solution of a deterministic sandpile model for arbitrary $N$, where $N$ is the size of a single toppling. The one- and two-point functions are given in term of the eigenvalues of an $N \times N$ transfer matrix. All the n-point functions can be found in the same way. Application of this method to a more general class of models is discussed. We also present a quantitative description of the limit cycle (attractor) as a multifractal.

cond-mat↗