Convex effective potential of $O(N)$-symmetric $ph{i}^4$ theory for large $N$

Abstract

We obtain effective potential of $O(N)$-symmetric ${\varphi }^4$ theory for large $N$ starting with a finite lattice system and taking the thermodynamic limit with great care. In the thermodynamic limit, it is globally real-valued and convex in both the symmetric and the broken phases. In particular, it has a flat bottom in the broken phase. Taking the continuum limit, we discuss renormalization effects to the flat bottom and exhibit the effective potential of the continuum theory in three and four dimensions.On the other hand the effective potential is nonconvex in a finite lattice system. Our numerical study shows that the barrier height of the effective potential flattens as a linear size of the system becomes large. It decreases obeying power law and the exponent is about $-2$. The result is clearly understood from dominance of configurations with slowly-rotating field in one direction.

New results on finite-size system are added. LaTeX, 21 pages, 6 figures

References in corpus (5)

• Topological Defects as Seeds for Eternal Inflation
• Symmetry Breaking and Finite Size Effects in Quantum Many-Body Systems
• Ground states of the infinite q-deformed Heisenberg ferromagnet
• The spectral gap of the ferromagnetic XXZ chain
• The Cutoff $\lambda {\varphi }^4$ O(N) Model in the Large N Limit

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• Constraint effective action and critical correlation functions at fixed magnetization
• Role of inhomogeneities in the flattening of the quantum effective potential