Frustration effects in antiferromagnets on planar random graphs

Abstract

We consider the effect of geometric frustration induced by the random distribution of loop lengths in the "fat" graphs of the dynamical triangulations model on coupled antiferromagnets. While the influence of such connectivity disorder is rather mild for ferromagnets in that an ordered phase persists and only the properties of the phase transition are substantially changed in some cases, any finite-temperature transition is wiped out due to frustration for some of the antiferromagnetic models. A wealth of different phenomena is observed: while for the annealed average of quantum gravity some graphs can adapt dynamically to allow the emergence of a Neel ordered phase, this is not possible for the quenched average, where a zero-temperature spin-glass phase appears instead. We relate the latter to the behaviour of conventional spin-glass models coupled to random graphs.

v3: 9 pages, 10 figures, RevTex4, two figures added, discussion of graph ensembles and disorder averages expanded, estimate of fractal dimension updated v2: 8 pages, 8 figures, RevTex4, two figures added, submitted to Phys. Rev. B v1: 16 pages, 6 figures

References in corpus (24)

• Statistical mechanics of complex networks
• Ising model in small-world networks
• Critical phenomena in networks
• Exact Solution of the O(n) Model on a Random Lattice
• Conformal Algebras of 2D Disordered Systems
• Conformal Invariance and SLE in Two-Dimensional Ising Spin Glasses
• Strong universality and algebraic scaling in two-dimensional Ising spin glasses
• Census of Planar Maps: From the One-Matrix Model Solution to a Combinatorial Proof
• A Numerical Test of KPZ Scaling: Potts Models Coupled to Two-Dimensional Quantum Gravity
• Correlation length of the two-dimensional Ising spin glass with bimodal interactions
• The Harris-Luck criterion for random lattices
• Ising model on 3D random lattices: A Monte Carlo study
• Quenched Random Graphs
• Ising Spins on Thin Graphs
• Potts Models on Feynman Diagrams
• Influence of the Ground-State Topology on the Domain-Wall Energy in the Edwards-Anderson +/- J Spin Glass Model
• Quenching 2D Quantum Gravity
• Ising and Potts Models on Quenched Random Gravity Graphs
• Finite-Size Scaling of the Domain Wall Entropy Distributions for the 2D $\pm J$ Ising Spin Glass
• Non-Self Averaging in Autocorrelations for Potts Models on Quenched Random Gravity Graphs
• The Wrong Kind of Gravity
• Search for Scaling Dimensions for Random Surfaces with c=1
• The XY Model on a Dynamical Random Lattice
• The F model on dynamical quadrangulations

Cited by in corpus (12)

• Fractal dimension of domain walls in two-dimensional Ising spin glasses
• Domain-wall excitations in the two-dimensional Ising spin glass
• Renormalization Group on hierarchical lattices in finite dimensional disordered Ising and Blume-Emery-Griffiths Models
• Zero-temperature phase of the XY spin glass in two dimensions: Genetic embedded matching heuristic
• Fractal dimension of domain walls in the Edwards-Anderson spin glass model
• Antiferromagnetic Ising model in scale-free networks
• Elementary excitations and the phase transition in the bimodal Ising spin glass model
• Ising Spin Glasses on Wheatstone-Bridge Hierarchical Lattices
• Site Percolation on Planar ${\Phi }^3$ Random Graphs
• Aspect-Ratio Scaling of Domain Wall Entropy for the 2D $\pm J$ Ising Spin Glass
• Boolean decision problems with competing interactions on scale-free networks: Critical thermodynamics
• Boolean decision problems with competing interactions on scale-free networks: Equilibrium and nonequilibrium behavior in an external bias