arXiv subjects

N. Theodorakopoulos

Publications and source records attributed to N. Theodorakopoulos.

4 recordsLinked to original sources

arXiv2005

Phase transitions in one dimension: are they all driven by domain walls?

Two known distinct examples of one-dimensional systems which are known to exhibit a phase transition are critically examined: (A) a lattice model with harmonic nearest-neighbor elastic interactions and an on-site Morse potential, and (B) the ferromagnetic, spin 1/2 Ising model with long-range pair interactions varying as the inverse square of the distance between pairs. In both cases it can be shown that the domain wall configurations become entropically stable at, or very near, the critical temperature. This might provide a "positive" criterion for the occurrence of a phase transition in one-dimensional systems.

cond-mat.stat-mech↗

arXiv2002

Critical dynamics of DNA denaturation

We present detailed molecular dynamics results for the displacement autocorrelation spectra of the Peyrard-Bishop model of thermal DNA denaturation. As the phase transition is approached, the spectra depend on whether the wavelength is smaller than, or exceeds the correlation length. In the first case, the spectra are dominated by a single peak, whose frequency approaches the bare acoustic frequency of the harmonic chain, and whose linewidth approaches zero as $T_c-T$. In the second case, a central peak (CP) feature is dominant, accounting for most of the weight; the linewidth of the CP appears to be temperature-independent. We also present force autocorrelation spectra which may be relevant for analyzing the statistical properties of localized modes.

cond-mat.stat-mech↗

arXiv2002

Phase transitions in homogeneous biopolymers: basic concepts and methods

The basic models of helix-coil transitions in biomolecules are introduced. These include phenomenological, zipper (Bragg-Zimm) models of polypeptides, loop-entropy (Poland-Scheraga) and Hamiltonian (Peyrard-Bishop) models of homogeneous DNA denaturation. The transfer integral approach to one-dimensional thermodynamics is presented in some detail, including the necessary extensions to deal with the singular integral equations arising in the case of on-site potentials with a flat top. The (non-)applicability of the theorems which prohibit phase transitions in one-dimensional systems is discussed.

cond-mat.stat-mech↗

arXiv1995

Nontopological thermal solitons in isotropic ferromagnetic lattices

The paper deals with the properties of thermally excited solitons of the isotropic spin-$S$ ferromagnetic chain with nearest-neighbor logarithmic interactions. The exact statistical mechanics of the interacting soliton gas is developed for the general case (arbitrary $S$, temperature and magnetic field). At low temperatures the model's thermodynamics coincides with that of the Heisenberg model. We present analytical approximations of the leading-order asymptotic behavior of the energy in three limiting cases: (a) zero field, low temperature, classical limit; (b) zero field, $T\to 0$, $S$ finite (quantum limit); (c) zero field, high temperature, classical limit. Cases (a) and (c) are examples of a dense gas of [non-topological] solitons; results are in agreement with those obtained by the transfer integral method. Case (b) illustrates the behavior of a dilute, yet strongly interacting soliton gas; results for the thermodynamics are very close to (but not identical with) spin-wave and/or Bethe-{\it Ansatz} predictions.

cond-mat↗