Spin Models on Dynamical Random Lattices

Spin models models living on suitable dynamical (connectivity) lattices give a toy model for gravity + matter systems that incorporates the back reaction between matter and geometry. In the 2D case some can be solved exactly via matrix model methods and critical exponents extracted for comparison with the numerical studies. 

• C. Baillie and D. Johnston, A Numerical Test of KPZ Scaling: Potts Models Coupled to 2D Quantum Gravity: Mod. Phys. Lett. A7, 1519-31, (1992)

• C. Baillie and D. Johnston, Multiple Potts Models Coupled to Two-Dimensional Quantum Gravity: Phys. Lett. B286, 44-52, (1992)

• C. Baillie and D. Johnston, The XY Model Coupled to Two-Dimensional Quantum Gravity: Phys. Lett. B291, 233-40, (1992)

• D. Johnston, Ising (anti-)ferromagnet on dynamical triangulations and quadrangulations: Phys. Lett. B314, 69-73, (1993)

• C. Baillie and D. Johnston, 2D O(3) model coupled to 2D Quantum Gravity: Phys. Rev. D49, 603-6, (1994)

• C. Baillie and D. Johnston, Damaging 2D Quantum Gravity: Phys. Lett. B326, 51-6, (1994)

• D. Johnston, Frustrating and Diluting Dynamical Lattice Ising Spins: Phys. Lett. B336, 229-36, (1994)

• C. Baillie and D. Johnston, Square Gravity: Phys. Lett. B357, 287-294, (1995)