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Distinct critical behaviors from the same state in quantum spin and population dynamics perspectives
C L Baldwin1,2, S Shivam3, S L Sondhi3
1National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA.
Physical Review. E
|February 19, 2021
Summary
Quantum spin systems and viral population dynamics share mathematical roots. Unexpected phase transition behaviors emerge when viewing spin models through a population dynamics lens, revealing new physics.
Area of Science:
- Statistical Mechanics
- Mathematical Biology
- Quantum Physics
Background:
- Ground states of transverse-field spin systems and late-time viral population distributions share mathematical similarities, both derived from a matrix's principal eigenvector.
- A key difference lies in the interpretation of this vector: wave-function amplitude in quantum spin models versus probability in population models.
Purpose of the Study:
- To investigate the consequences of the amplitude-versus-probability difference on phase transitions.
- To introduce a generalized model encompassing both spin and population dynamics.
- To explore new physics in established spin models when reinterpreted as population dynamics.
Main Methods:
- Analytical solution of a generalized mean-field model.
- Numerical analysis of one-dimensional spin chains with power-law interactions.
Main Results:
- Discontinuous phase transitions in spin systems become continuous under the population perspective.
- Continuous phase transitions in spin systems exhibit altered critical exponents when viewed as population dynamics.
- The generalized model provides an exact solution in the mean-field limit.
Conclusions:
- Reinterpreting quantum statistical mechanics spin models as population dynamics models reveals novel physical phenomena and critical behaviors.
- This cross-disciplinary approach offers new insights into both quantum systems and epidemiological modeling.
- Further research is motivated by the unexpected connections and potential for new discoveries.
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