Glass of directed polymers

Summary

I.      Directed polymers in random media (DPRM): 6 vertex model, transfer matrix (TM)

II.     One DPRM: free energy and its fluctuations

III.   Few DPRMs: Cost of non-crossing condition

IV.    (Vortex) Glass of DPRM: Results from Replica Bethe Ansatz

V.     Log(TM)/t eigenvalues compared to random matrices

 Open questions:

 Transition between  and  .

 Transition between edge and middle Log(eigenvalues).

 "Particle-hole" symmetry between smallest and largest Log(eigenvalues).

 Is the arrangemet of Log(eigenvalues) hyperuniform?

Acknowledgments

Abbas Saberi,    Sherry Chu,   Ramis Movassagh

Rutgers University                     127th Statistical Mechanics Conference                       December 15, 2024

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