We study the dissipative Hofstadter model on a triangular lattice, making use of the [Formula: see text] T-dual transformation of string theory. The [Formula: see text] dual transformation transcribes the model in a commutative basis into the model in a noncommutative basis. In the zero-temperature limit, the model exhibits an exact duality, which identifies equivalent points on the two-dimensional parameter space of the model. The exact duality also defines magic circles on the parameter space, where the model can be mapped onto the boundary sine-Gordon on a triangular lattice. The model describes the junction of three quantum wires in a uniform magnetic field background. An explicit expression of the equivalence relation, which identifies the points on the two-dimensional parameter space of the model by the exact duality, is obtained. It may help us to understand the structure of the phase diagram of the model.
Zero-temperature limit of the Kawasaki dynamics for the Ising lattice gas in a large two-dimensional torus