The role of random boundary conditions in spin systems

We develop a framework to simulate quantum field theories (QFTs) with boundaries in $(1+1)$ -dimenmsional curved spacetimes by employing open spin systems. Building upon our previous work that established a mapping from spin systems to QFTs in periodic geometries, we extend the correspondence to systems with boundaries, where boundary conditions play a crucial role in shaping the dynamics. Focusing on Majorana fermions, we derive the allowed boundary conditions from the requirement of inner product conservation and formulate their realization in spin systems. The corresponding spin model is shown to reproduce boundary conditions of QFT accurately when a free function in the spin model is appropriately chosen. As an explicit demonstration, we analyze a flat spacetime example, comparing spectra, mode functions, and linear responses between the continuum and lattice descriptions. Our findings confirm that open spin systems can successfully replicate QFT dynamics with boundaries.We develop a framework to simulate quantum field theories (QFTs) with boundaries in $(1+1)$-dimenmsional curved spacetimes by employing open spin systems. Building upon our previous work that established a mapping from spin systems to QFTs in periodic geometries, we extend the correspondence to systems with boundaries, where boundary conditions play a crucial role in shaping the dynamics. Focusing on Majorana fermions, we derive the allowed boundary conditions from the requirement of inner product conservation and formulate their realization in spin systems. The corresponding spin model is shown to reproduce boundary conditions of QFT accurately when a free function in the spin model is appropriately chosen. As an explicit demonstration, we analyze a flat spacetime example, comparing spectra, mode functions, and linear responses between the continuum and lattice descriptions. Our findings confirm that open spin systems can successfully replicate QFT dynamics with boundaries.

hep-thCross-listedarXiv:2602.17935Feb 23, 20260 citations

Chiral- and spin-correlation functions in a random-bondXYladder

Muriel Ney‐Nifle, H. J. Hilhorst, M A Moore

We analyze the role of discrete symmetry in a one-dimensional randomly frustrated XY model on a ladder lattice with \ifmmode\pm\else\textpm\fi{}J bonds. In the Villain formulation discrete-valued chiralities, associated with the plaquettes of the lattice, are decoupled from the continuous spin-wave variables. Within a low-temperature (T) approximation, we show that the chiralities and the XY spins have the same zero-T correlation-length exponent, which we determine exactly. We also show how this exponent follows from antiperiodic and reflecting boundary conditions imposed on a finite system at T=0. A contrast appears between the ladder and a two-dimensional picture recently proposed.We analyze the role of discrete symmetry in a one-dimensional randomly frustrated XY model on a ladder lattice with \ifmmode\pm\else\textpm\fi{}J bonds. In the Villain formulation discrete-valued chiralities, associated with the plaquettes of the lattice, are decoupled from the continuous spin-wave variables. Within a low-temperature (T) approximation, we show that the chiralities and the XY spins have the same zero-T correlation-length exponent, which we determine exactly. We also show how this exponent follows from antiperiodic and reflecting boundary conditions imposed on a finite system at T=0. A contrast appears between the ladder and a two-dimensional picture recently proposed.

Physical review. B, Condensed matterOct 1, 199312 citations

Effect of randomness on spin systems

Yutaka Okabe, Kazuhisa Kaneda, Yusuke Tomita +5 more

Jan 1, 19980 citations

We develop a framework to simulate quantum field theories (QFTs) with boundaries in

(1+1)

-dimenmsional curved spacetimes by employing open spin systems. Building upon our previous work that established a mapping from spin systems to QFTs in periodic geometries, we extend the correspondence to systems with boundaries, where boundary conditions play a crucial role in shaping the dynamics. Focusing on Majorana fermions, we derive the allowed boundary conditions from the requirement of inner product conservation and formulate their realization in spin systems. The corresponding spin model is shown to reproduce boundary conditions of QFT accurately when a free function in the spin model is appropriately chosen. As an explicit demonstration, we analyze a flat spacetime example, comparing spectra, mode functions, and linear responses between the continuum and lattice descriptions. Our findings confirm that open spin systems can successfully replicate QFT dynamics with boundaries.