This week my paper “Metamagnetism and zero-scale-factor universality in the two-dimensional J-Q model” came out in Physical Review B. This paper builds on my previous work studying the 1D J-Q model, focusing on the saturation transition at high magnetic field using quantum Monte Carlo and exact techniques.
Below a critical coupling value (Q/J)min, this saturation transition is continuous, and is an example of “zero-scale-factor” (ZSF) universality. In ZSF, the order parameter (in this case the magnetization) is described by a universal function of the bare coupling constants and no non-universal numbers (Sachdev, 1994). 2D is the upper critical dimension of ZSF, so we expect to see logarithmic violations of the scaling at low temperature. The form of these violations is predicted by Sachdev et al. This paper is the first numerical test of this form, and we find to our surprise that the logarithmic violations do not match the form proposed by Sachdev et al. The reasons for this are currently unclear and merit further investigation.
Above the coupling ratio (Q/J)min, the saturation transition take the form of a sudden magnetization jump an example of metamagnetism, a kind of first-order phase transition. This metamagnetic transition is broadly similar to the one discovered in our previous work on the 1D J-Q model (Iaizzi, 2017). It is caused by the onset of bound states of magnons (spin flips against a polarized background). Using an exact method, we extract the value of (Q/J)min.