Critical Behaviour of the Fuzzy Sphere

Understand

We study a multi-matrix model whose low temperature phase is a fuzzy sphere that undergoes an evaporation transition as the temperature is increased.

• We investigate finite size scaling of the system as the limiting temperature of stability of the fuzzy sphere phase is approached.
• We find on theoretical grounds that the system should obey scaling with specific heat exponent \alpha=1/2, shift exponent \bar \lambda=4/3 and that the peak in the specific heat grows with exponent \bar \omega=2/3.
• Using hybrid Monte Carlo simulations we find good collapse of specific heat data consistent with a scaling ansatz which give our best estimates for the scaling exponents as \alpha=0.50 \pm 0.01,\bar \lambda=1.41 \pm 0.08 and \bar \omega=0.66 \pm 0.08 .