Thouless–Anderson–Palmer Equations for the Multi-species Sherrington–Kirkpatrick Model

We prove the Thouless–Anderson–Palmer (TAP) equations for the local magnetization in the multi-species Sherrington–Kirkpatrick (MSK) spin glass model. One of the key ingredients is based on concentration results established in Dey and Wu (J Stat Phys 185(3):22, 2021). The equations hold at high temperature for general MSK model without positive semi-definite assumption on the variance profile matrix \(\mathbf {\Delta }^2\) ${\mathrm{\Delta }}^2$ .