Solutions for correlations along the coexistence curve and at the critical point of a kagom\'e lattice gas with three-particle interactions

We consider a two-dimensional (d=2) kagom\'e lattice gas model with attractive three-particle interactions around each triangular face of the kagom\'e lattice. Exact solutions are obtained for multiparticle correlations along the liquid and vapor branches of the coexistence curve and at criticality. The correlation solutions are also determined along the continuation of the curvilinear diameter of the coexistence region into the disordered fluid region. The method generates a linear algebraic system of correlation identities with coefficients dependent only upon the interaction parameter. Using a priori knowledge of pertinent solutions for the density and elementary triplet correlation, one finds a closed and linearly independent set of correlation identities defined upon a spatially compact nine-site cluster of the kagom\'e lattice. Resulting exact solution curves of the correlations are plotted and discussed as functions of the temperature, and are compared with corresponding results in a traditional kagom\'e lattice gas having nearest-neighbor pair interactions. An example of application for the multiparticle correlations is demonstrated in cavitation theory

Finite-size scaling and conformal anomaly of the Ising model in curved space

We study the finite-size scaling of the free energy of the Ising model on lattices with the topology of the tetrahedron and the octahedron. Our construction allows to perform changes in the length scale of the model without altering the distribution of the curvature in the space. We show that the subleading contribution to the free energy follows a logarithmic dependence, in agreement with the conformal field theory prediction. The conformal anomaly is given by the sum of the contributions computed at each of the conical singularities of the space, except when perfect order of the spins is precluded by frustration in the model.Comment: 4 pages, 4 Postscript figure

Ordering in Two-Dimensional Ising Models with Competing Interactions

We study the 2D Ising model on a square lattice with additional non-equal diagonal next-nearest neighbor interactions. The cases of classical and quantum (transverse) models are considered. Possible phases and their locations in the space of three Ising couplings are analyzed. In particular, incommensurate phases occurring only at non-equal diagonal couplings, are predicted. We also analyze a spin-pseudospin model comprised of the quantum Ising model coupled to XY spin chains in a particular region of interactions, corresponding to the Ising sector's super-antiferromagnetic (SAF) ground state. The spin-SAF transition in the coupled Ising-XY model into a phase with co-existent SAF Ising (pseudospin) long-range order and a spin gap is considered. Along with destruction of the quantum critical point of the Ising sector, the phase digram of the Ising-XY model can also demonstrate a re-entrance of the spin-SAF phase. A detailed study of the latter is presented. The mechanism of the re-entrance, due to interplay of interactions in the coupled model, and the conditions of its appearance are established. Applications of the spin-SAF theory for the transition in the quarter-filled ladder compound NaV2O5 are discussed.Comment: Minor revisions and refs. added; published version of the invited paper in a special issue of "Low Temp. Physics

Spinons in a Crossed-Chains Model of a 2D Spin Liquid

Using Random Phase Approximation, we show that a crossed-chains model of a spin-1/2 Heisenberg spins, with frustrated interchain couplings, has a non-dimerized spin-liquid ground state in 2D, with deconfined spinons as the elementary excitations. The results are confirmed by a bosonization study, which shows that the system is an example of a `sliding Luttinger liquid'. In an external field, the system develops an incommensurate field-induced long range order with a finite transition temperature.Comment: 4 pages, 3 figures; added references; scaling analysis, preserving spin rotational invariance, is extended to finite temperatur

Complex-Temperature Singularities in the d=2d=2 Ising Model. III. Honeycomb Lattice

We study complex-temperature properties of the uniform and staggered susceptibilities $\chi$ and $\chi^{(a)}$ of the Ising model on the honeycomb lattice. From an analysis of low-temperature series expansions, we find evidence that $\chi$ and $\chi^{(a)}$ both have divergent singularities at the point $z=-1 \equiv z_{\ell}$ (where $z=e^{-2K}$), with exponents $\gamma_{\ell}'= \gamma_{\ell,a}'=5/2$. The critical amplitudes at this singularity are calculated. Using exact results, we extract the behaviour of the magnetisation $M$ and specific heat $C$ at complex-temperature singularities. We find that, in addition to its zero at the physical critical point, $M$ diverges at $z=-1$ with exponent $\beta_{\ell}=-1/4$, vanishes continuously at $z=\pm i$ with exponent $\beta_s=3/8$, and vanishes discontinuously elsewhere along the boundary of the complex-temperature ferromagnetic phase. $C$ diverges at $z=-1$ with exponent $\alpha_{\ell}'=2$ and at $v=\pm i/\sqrt{3}$ (where $v = \tanh K$) with exponent $\alpha_e=1$, and diverges logarithmically at $z=\pm i$. We find that the exponent relation $\alpha'+2\beta+\gamma'=2$ is violated at $z=-1$; the right-hand side is 4 rather than 2. The connections of these results with complex-temperature properties of the Ising model on the triangular lattice are discussed.Comment: 22 pages, latex, figures appended after the end of the text as a compressed, uuencoded postscript fil

Reflections on the four facets of symmetry: how physics exemplifies rational thinking

In contemporary theoretical physics, the powerful notion of symmetry stands for a web of intricate meanings among which I identify four clusters associated with the notion of transformation, comprehension, invariance and projection. While their interrelations are examined closely, these four facets of symmetry are scrutinised one after the other in great detail. This decomposition allows us to examine closely the multiple different roles symmetry plays in many places in physics. Furthermore, some connections with others disciplines like neurobiology, epistemology, cognitive sciences and, not least, philosophy are proposed in an attempt to show that symmetry can be an organising principle also in these fields

The Ising Susceptibility Scaling Function

We have dramatically extended the zero field susceptibility series at both high and low temperature of the Ising model on the triangular and honeycomb lattices, and used these data and newly available further terms for the square lattice to calculate a number of terms in the scaling function expansion around both the ferromagnetic and, for the square and honeycomb lattices, the antiferromagnetic critical point.Comment: PDFLaTeX, 50 pages, 5 figures, zip file with series coefficients and background data in Maple format provided with the source files. Vs2: Added dedication and made several minor additions and corrections. Vs3: Minor corrections. Vs4: No change to eprint. Added essential square-lattice series input data (used in the calculation) that were removed from University of Melbourne's websit