Main results of Jacek Miękisz

Main results

Microscopic models of quasicrystals

Classical lattice-gas models without periodic ground-state configurations are generic
in the space of summable potentials.
with Charles Radin, Phys. Rev. B. 39: 1950-1952 (1989).
Fractal symmetry in an Ising model with a Thue-Morse ground state.
with C. Gardner, C. Radin and A. van Enter,
J. Phys. A.: Math. Gen. 22: L1019-L1023 (1989).
Construction of a classical lattice-gas model with a unique periodic ground state which is unstable
in nonzero temperatures. Quasicrystalline ground states are entropically stabilized in this model.
Commun. Math. Phys. 111: 533-538 (1987).
Period doubling of equilibrium states in a microscopic model of a quasicrystal.
J. Stat. Phys. 58: 1137-1149 (1990).
Construction of a finite-range lattice-gas model with a unique nonperiodic ground state
which is stable in a space of interactions.
J. Stat. Phys. 88: 691-711 (1997).
Construction of a finite-range classical lattice-gas model with a unique nonperiodic ground state
which is not a unique ground state of any nonfrustrated finite-range lattice-gas model.
J. Stat. Phys. 90: 285-300 (1998).
Construction of a lattice-gas model with a molecular devil's staircase.
with Janusz Jędrzejewski, J. Stat. Phys. 98, 589-620 (2000).

with Janusz Jędrzejewski, Europhysics Letters 50: 307-311 (2000).

Stochastic models of evolutionary games

Ensemble stability in stochastic models of spatial games with many players,
noise level versus the number of players. Abstract, Paper
Equilibrium selection in stochastic adaptive games with many players. Abstract, Paper
Classification of symmetric three-player games with two strategies,
stability of their Nash equlibria. Abstract, Paper