It is shown that the Luttinger liquid is unstable to arbitrarily small transverse hopping. The crossover temperatures below which either transverse coherent band motion or long-range order start to develop can be finite even when spin and charge velocities differ. Explicit scaling relations for the one-particle and two-particle crossover temperatures are derived in terms of transverse hopping, spin and charge velocities, and anomalous exponents. The special case of infinite-range transverse hopping is treated exactly and yields a Fermi liquid down to $T=0\mathrm{}$, unless the anomalous exponent $\theta >1\mathrm{}$.

• Received 5 July 1994

DOI:https://doi.org/10.1103/PhysRevLett.74.968