Competing interactions in a long-range spin-lattice coupled model and tricriticality

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Materials Science

Background:

• Strongly correlated systems exhibit complex critical behavior during magnetic phase transitions.
• The interplay between spin and lattice degrees of freedom is crucial for understanding these transitions.
• Analytical methods are needed to model these phenomena effectively.

Purpose of the Study:

• To construct an effective model Hamiltonian for studying magnetic phase transitions.
• To investigate the role of order parameter-strain field coupling.
• To analyze the impact of long-range (LR) and short-range interactions on critical behavior.

Main Methods:

• Development of a C-type model Hamiltonian.
• Renormalization-group analysis at one-loop order.
• Investigation of competing short-range interactions and nonlocal theories.

Main Results:

• Identification of non-trivial critical behavior governed by an LR fixed point.
• Demonstration of differing critical behavior with competing short-range interactions.
• Observation of first-order instability signatures in purely nonlocal theories.

Conclusions:

• The model effectively captures critical phenomena in strongly correlated systems.
• Long-range strain interactions significantly influence magnetic phase transitions.
• Further applicability in explaining experimental results is discussed.