Anisotropic Long-Range Spin Systems

Understand

We consider anisotropic long-range interacting spin systems in $d$ dimensions.

• The interaction between the spins decays with the distance as a power law with different exponents in different directions: we consider an exponent $d_{1}+\sigma_1$ in $d_1$ directions and another exponent $d_{2}+\sigma_2$ in the remaining $d_2\equiv d-d_1$ ones.
• We introduce a low energy effective action with non analytic power of the momenta.
• As a function of the two exponents $\sigma_1$ and $\sigma_2$ we show the system to have three different regimes, two where it is actually anisotropic and one where the isotropy is finally restored.