Scaling theory of antiferromagnetic Heisenberg ladder models

The S=1/2 antiferromagnetic Heisenberg model on multi-leg ladders is investigated. Criticality of the ground-state transition is explored by means of finite-size scaling. The ladders with an even number of legs and those with an odd number of legs are distinguished clearly. In the former, the energy gap opens up as Delta E approximately J_{perpendicular to}, where J _{perpendicular to} is the strength of the antiferromagnetic inter-chain coupling. In the latter, the critical phase with the central charge c=1 extends over the whole region of J perpendicular to >0.