Renormalization-group treatment of a Potts lattice gas for krypton adsorbed onto graphite

Abstract

Kryptori atoms adsorbed in submonolayer quantities onto the basal graphite surface may be represented by a triangular lattice gas with nearest-neighbor exclusion and further-neighbor attraction decreasing with separation. %'e view this as a three-state Potts model with thermodynamic vacancies which are controlled by a chemical potential. A position-space renormalization-group treatment is performed by adapting Migdal's approximate recursion to the triangular lattice, and results are compared with experimental data. Our temperature versus density phase diagram for krypton submonolayers has an in-registry solid phase separated from a liquid phase by a line of continuous {Potts tricritical) transitions at higher temperatures. At lower temperatures, the solid phase is separated from a gas phase by first-order transitions. The Potts tricritical line meets the coexistence region of the f&rst-order transitions at an isolated fourth-order transition point. This point may be related to the transition of the triplet Ising model, solved exactly by Baxter and %'u. Our "Potts lattice gas" global phase diagram is in a three-parameter space of pair-interaction constants and chemical potential. It contains solid, liquid, and gas phases, variously separated by first-order, Ising critical, threeand four-state Potts, and fourth-order transitions. The Lennard-Jones potential between krypton adatoms determines the planar subspace applicable to krypton subrnonolayers. Other planes, similarly determined, are applicable to adsorbed nitrogen, methane, and ethane, for which we estir»ate the temperatures of the foUrth-order points. Our treatment also predicts a tricfitical end-point topology, instead of the fourth-order point topology, when second-neighbor adatom pair attraction is not much stronger than thirdand fourth-neighbor attractions.

Chiral Potts spin glass ind=2and 3 dimensions

“…This approximation for the cubic lattice is an uncontrolled approximation, as in fact are all renormalization-group theory calculations in d = 3 and all mean-field theory calculations. However, as noted before [45], the local summation in position-space technique used here has been qualitatively, near-quantitatively, and predictively successful in a large variety of problems, such as arbitrary spin-s Ising models [46], global BlumeEmery-Griffiths model [47], first-and second-order Potts transitions [48,49], antiferromagnetic Potts critical phases [50,51], ordering [6] and superfluidity [52] on surfaces, multiply reentrant liquid crystal phases [53,54], chaotic spin glasses [55], random-field [56,57] and random-temperature [58,59] magnets, including the remarkably small d = 3 magnetization critical exponent β of the random-field Ising model, and high-temperature superconductors [60]. Thus, this renormalization-group approximation continues to be widely used [61][62][63][64][65][66][67][68][69][70][71][72][73][74].…”

“…The upper and lower subscripts of J ± > 0 give left-handed and right-handed chirality (corresponding to heavy and superheavy domain walls in the krypton-on-graphite incommensurate ordering [2,5]), whereas J ± = 0 gives the nonchiral Potts model (relevant to the krypton-on-graphite epitaxial ordering [6]). …”

“…The starting trimodal quenched probability distribution of the interactions, characterized by p and c as described above, is not conserved under rescaling. The renormalized quenched probability distribution of the interactions is obtained by the convolution [75] (6) where J ≡ (J 0 ,J + ,J − ) and R({J(ij )}) represents the bond decimation and bond moving given in Eqs. (4) and (5).…”

Stepwise positional-orientational order and the multicritical-multistructural global phase diagram of thes=3/2Ising model from renormalization-group theory

“…This approximation for the cubic lattice is an uncontrolled approximation, as in fact are all renormalization-group theory calculations in d = 3 and all mean-field theory calculations. However, the local summation in position-space technique used here has been qualitatively, near-quantitatively, and predictively successful in a large variety of problems, such as arbitrary spin-s Ising models [73], global Blume-Emery-Griffiths models [2], first-and second-order Potts transitions [74,75], antiferromagnetic Potts critical phases [76], ordering [77] and superfluidity [78] on surfaces, multiply reentrant liquid crystal phases [79,80], chaotic spin glasses [81], random-field [82] and random-temperature [83] magnets, and high-temperature superconductors [84].…”

Island formation and condensation of a chemisorbed overlayer

“…Since in such a system, whether it is ordered or not, an overlAyer atom will always be found (except near the desorption temperature) in a prescribed localized site that has a definite coordinate vector with respect to some origin, a lattice gas model can be used to study such properties of the overlayer as phase andovelayr oderng. (1)(2)(3)(4) transitions, diffusion, and overlayer ordering.…”