pbc_lattice.hpp

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/// @file spatial/pbc_lattice.hpp
/// @brief Precomputed periodic-boundary neighbor arrays for a 2D square lattice.
///
/// PBCLattice2D builds up[i], dn[i], lt[i], rt[i] once from modulo arithmetic
/// so the hot-path (Metropolis sweeps, BFS cluster detection) never calls %.
///
/// Flat layout: i = row * N + col,  row and col in [0, N).
#pragma once
 
#include <vector>
 
namespace num {
 
/// 4-neighbor periodic-boundary index arrays for an N×N lattice.
struct PBCLattice2D {
    int N;                            ///< Side length; total sites = N*N
    std::vector<int> up, dn, lt, rt;  ///< up/dn = row±1, lt/rt = col±1 (PBC)
 
    explicit PBCLattice2D(int N)
        : N(N), up(N*N), dn(N*N), lt(N*N), rt(N*N)
    {
        for (int row = 0; row < N; ++row)
            for (int col = 0; col < N; ++col) {
                const int i = row * N + col;
                up[i] = ((row - 1 + N) % N) * N + col;
                dn[i] = ((row + 1)     % N) * N + col;
                lt[i] = row * N + (col - 1 + N) % N;
                rt[i] = row * N + (col + 1)     % N;
            }
    }
};
 
} // namespace num