arXiv subjects

L. Samaj

Publications and source records attributed to L. Samaj.

41 records · Page 3Linked to original sources

arXiv2002

Exact Solution of a Charge-Asymmetric Two-Dimensional Coulomb Gas

The model under consideration is an asymmetric two-dimensional Coulomb gas of positively (q_1=+1) and negatively (q_2=-1/2) charged pointlike particles, interacting via a logarithmic potential. This continuous system is stable against collapse of positive-negative pairs of charges for the dimensionless coupling constant (inverse temperature) β<4. The mapping of the Coulomb gas is made onto the complex Bullough-Dodd model, and recent results about that integrable 2D field theory are used. The mapping provides the full thermodynamics (the free energy, the internal energy, the specific heat) and the large-distance asymptotics of the particle correlation functions, in the whole stability regime of the plasma. The results are checked by a small-βexpansion and close to the collapse β=4 point. The comparison is made with the exactly solvable symmetric version of the model (q_1=+1, q_2=-1), and some fundamental changes in statistics caused by the charge asymmetry are pointed out.

cond-mat.stat-mech↗

arXiv2001

Thermodynamic Properties of the Two-Dimensional Coulomb Gas in the Low-Density Limit

The model under consideration is the two-dimensional Coulomb gas of $\pm$ charged hard disks with diameter $σ$. For the case of pointlike charges $(σ=0)$, the system is stable against collapse of positive-negative pairs of charges in the range of inverse temperatures $0 \le β< 2$, where its full thermodynamics was obtained exactly [L. {Š}amaj and I. Trav{ě}nec, {\it J. Stat. Phys.} {\bf 101}:713 (2000)]. In the present work, we derive the leading correction to the exact thermodynamics of pointlike charges due to the presence of the hard core $σ$ (appearing in the dimensionless combination $nσ^2$, $n$ is the particle density). This permits us to extend the treatment to the interval $2\le β<3$ (the Kosterlitz-Thouless phase transition takes place at $β=4$). The results, which are exact in the low-density limit $nσ^2 \to 0$, reproduce correctly the singularities of thermodynamic quantities at the collapse point $β=2$ and agree very well with Monte-Carlo simulations.

cond-mat.stat-mech↗

arXiv2000

Another Derivation of a Sum Rule for the Two-Dimensional Two-Component Plasma

In a two-dimensional two-component plasma, the second moment of the number density correlation function has the simple value $\{12 π[1-(Γ/4)]^2\}^{-1}$, where $Γ$ is the dimensionless coupling constant. This result is derived directly by using diagrammatic methods.

cond-mat.stat-mech↗

arXiv1999

The Sixth-Moment Sum Rule For the Pair Correlations of the Two-Dimensional One-Component Plasma: Exact Result

The system under consideration is a two-dimensional one-component plasma in fluid regime, at density n and at arbitrary coupling Gamma=beta e^2 (e=unit charge, beta = inverse temperature). The Helmholtz free energy of the model, as the generating functional for the direct pair correlation c, is treated in terms of a convergent renormalized Mayer diagrammatic expansion in density. Using specific topological transformations within the bond-renormalized Mayer expansion we prove that the nonzero contributions to the regular part of the Fourier component of c up to the k^2-term originate exclusively from the ring diagrams (unable to undertake the bond-renormalization procedure) of the Helmholtz free energy. In particular, c(k)=-Gamma/k^2 + Gamma/(8 pi n) - k^2/[96(pi n)^2] + O(k^4). This result fixes via the Ornstein-Zernike relation, besides the well-known zeroth-, second- and fourth- moment sum rules, the new six-momnt condition for the truncated pair correlation h, n(pi Gamma n/2)^3 Integral r^6 h(r) d^2 r = 3(Gamma-6)(8-3 Gamma)/4.

cond-mat.stat-mech↗

arXiv1997

Ordering and Demixing Transitions in Multicomponent Widom-Rowlinson Models

We use Monte Carlo techniques and analytical methods to study the phase diagram of multicomponent Widom-Rowlinson models on a square lattice: there are M species all with the same fugacity z and a nearest neighbor hard core exclusion between unlike particles. Simulations show that for M between two and six there is a direct transition from the gas phase at z < z_d (M) to a demixed phase consisting mostly of one species at z > z_d (M) while for M \geq 7 there is an intermediate ``crystal phase'' for z lying between z_c(M) and z_d(M). In this phase, which is driven by entropy, particles, independent of species, preferentially occupy one of the sublattices, i.e. spatial symmetry but not particle symmetry is broken. The transition at z_d(M) appears to be first order for M \geq 5 putting it in the Potts model universality class. For large M the transition between the crystalline and demixed phase at z_d(M) can be proven to be first order with z_d(M) \sim M-2 + 1/M + ..., while z_c(M) is argued to behave as μ_{cr}/M, with μ_{cr} the value of the fugacity at which the one component hard square lattice gas has a transition, and to be always of the Ising type. Explicit calculations for the Bethe lattice with the coordination number q=4 give results similar to those for the square lattice except that the transition at z_d(M) becomes first order at M>2. This happens for all q, consistent with the model being in the Potts universality class.

cond-mat.stat-mech↗